Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 74.5% → 83.5%

Time: 18.2s

Alternatives: 23

Speedup: 0.9×

• 57.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
  (* j (- (* c t) (* i y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 74.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
  (* j (- (* c t) (* i y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 83.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot \mathsf{fma}\left(-z, \frac{b}{t}, j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
          (* j (- (* t c) (* y i))))))
   (if (<= t_1 INFINITY) t_1 (* c (* t (fma (- z) (/ b t) j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = c * (t * fma(-z, (b / t), j));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c)))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(t * fma(Float64(-z), Float64(b / t), j)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(c * N[(t * N[((-z) * N[(b / t), $MachinePrecision] + j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < +inf.0

   1. Initial program 93.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   if +inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))))

   1. Initial program 0.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) - \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. mul-1-neg N/A

         \[\leadsto \left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) - \color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot \left(b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. cancel-sign-sub N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) + a \cdot \left(b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(z \cdot \left(x \cdot y - b \cdot c\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} + a \cdot \left(b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(x \cdot y - b \cdot c\right) + \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(b \cdot i\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. cancel-sign-sub N/A

         \[\leadsto \left(z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. associate-*r* N/A

         \[\leadsto \left(z \cdot \left(x \cdot y - b \cdot c\right) + \left(\color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(b \cdot i\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      8. mul-1-neg N/A

         \[\leadsto \left(z \cdot \left(x \cdot y - b \cdot c\right) + \left(\left(-1 \cdot a\right) \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot a\right)} \cdot \left(b \cdot i\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      9. distribute-lft-out-- N/A

         \[\leadsto \left(z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto \left(z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{\left(a \cdot -1\right)} \cdot \left(t \cdot x - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      11. associate-*r* N/A

          \[\leadsto \left(z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      12. distribute-lft-out-- N/A

          \[\leadsto \left(z \cdot \left(x \cdot y - b \cdot c\right) + a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(z, x \cdot y - b \cdot c, a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 34.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \mathsf{fma}\left(c, -b, y \cdot x\right), a \cdot \mathsf{fma}\left(t, -x, i \cdot b\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(-1 \cdot \left(b \cdot z\right) + j \cdot t\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(-1 \cdot \left(b \cdot z\right) + j \cdot t\right)} \]

      2. +-commutative N/A

         \[\leadsto c \cdot \color{blue}{\left(j \cdot t + -1 \cdot \left(b \cdot z\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} + -1 \cdot \left(b \cdot z\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto c \cdot \color{blue}{\mathsf{fma}\left(t, j, -1 \cdot \left(b \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto c \cdot \mathsf{fma}\left(t, j, \color{blue}{\mathsf{neg}\left(b \cdot z\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto c \cdot \mathsf{fma}\left(t, j, \color{blue}{b \cdot \left(\mathsf{neg}\left(z\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto c \cdot \mathsf{fma}\left(t, j, b \cdot \color{blue}{\left(-1 \cdot z\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto c \cdot \mathsf{fma}\left(t, j, \color{blue}{b \cdot \left(-1 \cdot z\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto c \cdot \mathsf{fma}\left(t, j, b \cdot \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right) \]

      10. lower-neg.f64 49.7

          \[\leadsto c \cdot \mathsf{fma}\left(t, j, b \cdot \color{blue}{\left(-z\right)}\right) \]

   8. Simplified 49.7%

      \[\leadsto \color{blue}{c \cdot \mathsf{fma}\left(t, j, b \cdot \left(-z\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(j + -1 \cdot \frac{b \cdot z}{t}\right)\right)} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(-1 \cdot \frac{b \cdot z}{t} + j\right)}\right) \]

       2. mul-1-neg N/A

          \[\leadsto c \cdot \left(t \cdot \left(\color{blue}{\left(\mathsf{neg}\left(\frac{b \cdot z}{t}\right)\right)} + j\right)\right) \]

       3. neg-sub0 N/A

          \[\leadsto c \cdot \left(t \cdot \left(\color{blue}{\left(0 - \frac{b \cdot z}{t}\right)} + j\right)\right) \]

       4. associate-+l- N/A

          \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(0 - \left(\frac{b \cdot z}{t} - j\right)\right)}\right) \]

       5. unsub-neg N/A

          \[\leadsto c \cdot \left(t \cdot \left(0 - \color{blue}{\left(\frac{b \cdot z}{t} + \left(\mathsf{neg}\left(j\right)\right)\right)}\right)\right) \]

       6. mul-1-neg N/A

          \[\leadsto c \cdot \left(t \cdot \left(0 - \left(\frac{b \cdot z}{t} + \color{blue}{-1 \cdot j}\right)\right)\right) \]

       7. +-commutative N/A

          \[\leadsto c \cdot \left(t \cdot \left(0 - \color{blue}{\left(-1 \cdot j + \frac{b \cdot z}{t}\right)}\right)\right) \]

       8. neg-sub0 N/A

          \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot j + \frac{b \cdot z}{t}\right)\right)\right)}\right) \]

       9. lower-*.f64 N/A

          \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(\mathsf{neg}\left(\left(-1 \cdot j + \frac{b \cdot z}{t}\right)\right)\right)\right)} \]

       10. neg-sub0 N/A

           \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(0 - \left(-1 \cdot j + \frac{b \cdot z}{t}\right)\right)}\right) \]

       11. +-commutative N/A

           \[\leadsto c \cdot \left(t \cdot \left(0 - \color{blue}{\left(\frac{b \cdot z}{t} + -1 \cdot j\right)}\right)\right) \]

       12. mul-1-neg N/A

           \[\leadsto c \cdot \left(t \cdot \left(0 - \left(\frac{b \cdot z}{t} + \color{blue}{\left(\mathsf{neg}\left(j\right)\right)}\right)\right)\right) \]

       13. unsub-neg N/A

           \[\leadsto c \cdot \left(t \cdot \left(0 - \color{blue}{\left(\frac{b \cdot z}{t} - j\right)}\right)\right) \]

       14. associate-+l- N/A

           \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(\left(0 - \frac{b \cdot z}{t}\right) + j\right)}\right) \]

       15. neg-sub0 N/A

           \[\leadsto c \cdot \left(t \cdot \left(\color{blue}{\left(\mathsf{neg}\left(\frac{b \cdot z}{t}\right)\right)} + j\right)\right) \]

       16. *-commutative N/A

           \[\leadsto c \cdot \left(t \cdot \left(\left(\mathsf{neg}\left(\frac{\color{blue}{z \cdot b}}{t}\right)\right) + j\right)\right) \]

       17. associate-/l* N/A

           \[\leadsto c \cdot \left(t \cdot \left(\left(\mathsf{neg}\left(\color{blue}{z \cdot \frac{b}{t}}\right)\right) + j\right)\right) \]

       18. distribute-lft-neg-in N/A

           \[\leadsto c \cdot \left(t \cdot \left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot \frac{b}{t}} + j\right)\right) \]

       19. mul-1-neg N/A

           \[\leadsto c \cdot \left(t \cdot \left(\color{blue}{\left(-1 \cdot z\right)} \cdot \frac{b}{t} + j\right)\right) \]

       20. lower-fma.f64 N/A

           \[\leadsto c \cdot \left(t \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot z, \frac{b}{t}, j\right)}\right) \]

   11. Simplified 53.6%

       \[\leadsto c \cdot \color{blue}{\left(t \cdot \mathsf{fma}\left(-z, \frac{b}{t}, j\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot \mathsf{fma}\left(-z, \frac{b}{t}, j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 76.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.7 \cdot 10^{-19}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot \left(-c\right), b, \mathsf{fma}\left(b, a \cdot i, y \cdot \mathsf{fma}\left(-j, i, x \cdot z\right)\right)\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+167}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \mathsf{fma}\left(z, \mathsf{fma}\left(c, -b, x \cdot y\right), a \cdot \mathsf{fma}\left(t, -x, b \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \mathsf{fma}\left(j, -i, x \cdot z\right), -b \cdot \left(z \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -6.7e-19)
   (fma (* z (- c)) b (fma b (* a i) (* y (fma (- j) i (* x z)))))
   (if (<= y 6.2e+167)
     (+
      (* j (- (* t c) (* y i)))
      (fma z (fma c (- b) (* x y)) (* a (fma t (- x) (* b i)))))
     (fma y (fma j (- i) (* x z)) (- (* b (* z c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -6.7e-19) {
		tmp = fma((z * -c), b, fma(b, (a * i), (y * fma(-j, i, (x * z)))));
	} else if (y <= 6.2e+167) {
		tmp = (j * ((t * c) - (y * i))) + fma(z, fma(c, -b, (x * y)), (a * fma(t, -x, (b * i))));
	} else {
		tmp = fma(y, fma(j, -i, (x * z)), -(b * (z * c)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -6.7e-19)
		tmp = fma(Float64(z * Float64(-c)), b, fma(b, Float64(a * i), Float64(y * fma(Float64(-j), i, Float64(x * z)))));
	elseif (y <= 6.2e+167)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + fma(z, fma(c, Float64(-b), Float64(x * y)), Float64(a * fma(t, Float64(-x), Float64(b * i)))));
	else
		tmp = fma(y, fma(j, Float64(-i), Float64(x * z)), Float64(-Float64(b * Float64(z * c))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -6.7e-19], N[(N[(z * (-c)), $MachinePrecision] * b + N[(b * N[(a * i), $MachinePrecision] + N[(y * N[((-j) * i + N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e+167], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(c * (-b) + N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(t * (-x) + N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(j * (-i) + N[(x * z), $MachinePrecision]), $MachinePrecision] + (-N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.69999999999999998e-19

   1. Initial program 64.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      6. distribute-rgt-in N/A

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, -1 \cdot \left(i \cdot j\right) + x \cdot z, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right)} \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(-1 \cdot i\right) \cdot j} + x \cdot z, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{j \cdot \left(-1 \cdot i\right)} + x \cdot z, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(j, -1 \cdot i, x \cdot z\right)}, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      11. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \color{blue}{\mathsf{neg}\left(i\right)}, x \cdot z\right), \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      12. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \color{blue}{\mathsf{neg}\left(i\right)}, x \cdot z\right), \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), \color{blue}{z \cdot x}\right), \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), \color{blue}{z \cdot x}\right), \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      15. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), \color{blue}{b \cdot \left(\mathsf{neg}\left(\left(c \cdot z - a \cdot i\right)\right)\right)}\right) \]

      16. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), b \cdot \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), \color{blue}{b \cdot \left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)}\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - a \cdot i\right)\right)\right)}\right) \]

      19. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), b \cdot \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z + \left(\mathsf{neg}\left(a \cdot i\right)\right)\right)}\right)\right)\right) \]

   5. Simplified 80.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \mathsf{fma}\left(j, -i, z \cdot x\right), b \cdot \mathsf{fma}\left(c, -z, i \cdot a\right)\right)} \]
   6. Step-by-step derivation

      1. lift-neg.f64 N/A

         \[\leadsto y \cdot \left(j \cdot \color{blue}{\left(\mathsf{neg}\left(i\right)\right)} + z \cdot x\right) + b \cdot \left(c \cdot \left(\mathsf{neg}\left(z\right)\right) + i \cdot a\right) \]

      2. lift-*.f64 N/A

         \[\leadsto y \cdot \left(j \cdot \left(\mathsf{neg}\left(i\right)\right) + \color{blue}{z \cdot x}\right) + b \cdot \left(c \cdot \left(\mathsf{neg}\left(z\right)\right) + i \cdot a\right) \]

      3. lift-fma.f64 N/A

         \[\leadsto y \cdot \color{blue}{\mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right)} + b \cdot \left(c \cdot \left(\mathsf{neg}\left(z\right)\right) + i \cdot a\right) \]

      4. lift-neg.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right) + b \cdot \left(c \cdot \color{blue}{\left(\mathsf{neg}\left(z\right)\right)} + i \cdot a\right) \]

      5. lift-*.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right) + b \cdot \left(c \cdot \left(\mathsf{neg}\left(z\right)\right) + \color{blue}{i \cdot a}\right) \]

      6. lift-fma.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right) + b \cdot \color{blue}{\mathsf{fma}\left(c, \mathsf{neg}\left(z\right), i \cdot a\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right) + \color{blue}{b \cdot \mathsf{fma}\left(c, \mathsf{neg}\left(z\right), i \cdot a\right)} \]

      8. +-commutative N/A

         \[\leadsto \color{blue}{b \cdot \mathsf{fma}\left(c, \mathsf{neg}\left(z\right), i \cdot a\right) + y \cdot \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \mathsf{fma}\left(c, \mathsf{neg}\left(z\right), i \cdot a\right)} + y \cdot \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right) \]

      10. lift-fma.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(\mathsf{neg}\left(z\right)\right) + i \cdot a\right)} + y \cdot \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right) \]

      11. distribute-rgt-in N/A

          \[\leadsto \color{blue}{\left(\left(c \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot b + \left(i \cdot a\right) \cdot b\right)} + y \cdot \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right) \]

      12. associate-+l+ N/A

          \[\leadsto \color{blue}{\left(c \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot b + \left(\left(i \cdot a\right) \cdot b + y \cdot \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right)\right)} \]

      13. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(c \cdot \left(\mathsf{neg}\left(z\right)\right), b, \left(i \cdot a\right) \cdot b + y \cdot \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right)\right)} \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{c \cdot \left(\mathsf{neg}\left(z\right)\right)}, b, \left(i \cdot a\right) \cdot b + y \cdot \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right)\right) \]

   7. Applied egg-rr 82.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c \cdot \left(-z\right), b, \mathsf{fma}\left(b, a \cdot i, y \cdot \mathsf{fma}\left(-j, i, z \cdot x\right)\right)\right)} \]

   if -6.69999999999999998e-19 < y < 6.1999999999999999e167

   1. Initial program 82.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) - \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. mul-1-neg N/A

         \[\leadsto \left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) - \color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot \left(b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. cancel-sign-sub N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) + a \cdot \left(b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(z \cdot \left(x \cdot y - b \cdot c\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} + a \cdot \left(b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(x \cdot y - b \cdot c\right) + \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(b \cdot i\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. cancel-sign-sub N/A

         \[\leadsto \left(z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. associate-*r* N/A

         \[\leadsto \left(z \cdot \left(x \cdot y - b \cdot c\right) + \left(\color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(b \cdot i\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      8. mul-1-neg N/A

         \[\leadsto \left(z \cdot \left(x \cdot y - b \cdot c\right) + \left(\left(-1 \cdot a\right) \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot a\right)} \cdot \left(b \cdot i\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      9. distribute-lft-out-- N/A

         \[\leadsto \left(z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto \left(z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{\left(a \cdot -1\right)} \cdot \left(t \cdot x - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      11. associate-*r* N/A

          \[\leadsto \left(z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      12. distribute-lft-out-- N/A

          \[\leadsto \left(z \cdot \left(x \cdot y - b \cdot c\right) + a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(z, x \cdot y - b \cdot c, a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 85.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \mathsf{fma}\left(c, -b, y \cdot x\right), a \cdot \mathsf{fma}\left(t, -x, i \cdot b\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if 6.1999999999999999e167 < y

   1. Initial program 67.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      6. distribute-rgt-in N/A

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, -1 \cdot \left(i \cdot j\right) + x \cdot z, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right)} \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(-1 \cdot i\right) \cdot j} + x \cdot z, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{j \cdot \left(-1 \cdot i\right)} + x \cdot z, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(j, -1 \cdot i, x \cdot z\right)}, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      11. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \color{blue}{\mathsf{neg}\left(i\right)}, x \cdot z\right), \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      12. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \color{blue}{\mathsf{neg}\left(i\right)}, x \cdot z\right), \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), \color{blue}{z \cdot x}\right), \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), \color{blue}{z \cdot x}\right), \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      15. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), \color{blue}{b \cdot \left(\mathsf{neg}\left(\left(c \cdot z - a \cdot i\right)\right)\right)}\right) \]

      16. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), b \cdot \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), \color{blue}{b \cdot \left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)}\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - a \cdot i\right)\right)\right)}\right) \]

      19. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), b \cdot \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z + \left(\mathsf{neg}\left(a \cdot i\right)\right)\right)}\right)\right)\right) \]

   5. Simplified 76.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \mathsf{fma}\left(j, -i, z \cdot x\right), b \cdot \mathsf{fma}\left(c, -z, i \cdot a\right)\right)} \]

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), \color{blue}{\mathsf{neg}\left(b \cdot \left(c \cdot z\right)\right)}\right) \]

      2. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), \color{blue}{b \cdot \left(\mathsf{neg}\left(c \cdot z\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), b \cdot \color{blue}{\left(-1 \cdot \left(c \cdot z\right)\right)}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), \color{blue}{b \cdot \left(-1 \cdot \left(c \cdot z\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), b \cdot \color{blue}{\left(\mathsf{neg}\left(c \cdot z\right)\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), b \cdot \color{blue}{\left(c \cdot \left(\mathsf{neg}\left(z\right)\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), b \cdot \left(c \cdot \color{blue}{\left(-1 \cdot z\right)}\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), b \cdot \color{blue}{\left(c \cdot \left(-1 \cdot z\right)\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), b \cdot \left(c \cdot \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right) \]

      10. lower-neg.f64 88.2

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, -i, z \cdot x\right), b \cdot \left(c \cdot \color{blue}{\left(-z\right)}\right)\right) \]

   8. Simplified 88.2%

      \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, -i, z \cdot x\right), \color{blue}{b \cdot \left(c \cdot \left(-z\right)\right)}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.7 \cdot 10^{-19}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot \left(-c\right), b, \mathsf{fma}\left(b, a \cdot i, y \cdot \mathsf{fma}\left(-j, i, x \cdot z\right)\right)\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+167}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \mathsf{fma}\left(z, \mathsf{fma}\left(c, -b, x \cdot y\right), a \cdot \mathsf{fma}\left(t, -x, b \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \mathsf{fma}\left(j, -i, x \cdot z\right), -b \cdot \left(z \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.04 \cdot 10^{+124}:\\ \;\;\;\;j \cdot \mathsf{fma}\left(c, t, -y \cdot i\right)\\ \mathbf{elif}\;j \leq -5.7 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-221}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \mathsf{fma}\left(a, \frac{i}{z}, -c\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(\mathsf{fma}\left(i, \frac{y}{t}, -c\right) \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -1.04e+124)
   (* j (fma c t (- (* y i))))
   (if (<= j -5.7e+32)
     (+ (* y (* x z)) (* j (* t c)))
     (if (<= j -6e-221)
       (* (* z b) (fma a (/ i z) (- c)))
       (if (<= j 2.8e-16)
         (* x (- (* y z) (* t a)))
         (* j (* (fma i (/ y t) (- c)) (- t))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.04e+124) {
		tmp = j * fma(c, t, -(y * i));
	} else if (j <= -5.7e+32) {
		tmp = (y * (x * z)) + (j * (t * c));
	} else if (j <= -6e-221) {
		tmp = (z * b) * fma(a, (i / z), -c);
	} else if (j <= 2.8e-16) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = j * (fma(i, (y / t), -c) * -t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -1.04e+124)
		tmp = Float64(j * fma(c, t, Float64(-Float64(y * i))));
	elseif (j <= -5.7e+32)
		tmp = Float64(Float64(y * Float64(x * z)) + Float64(j * Float64(t * c)));
	elseif (j <= -6e-221)
		tmp = Float64(Float64(z * b) * fma(a, Float64(i / z), Float64(-c)));
	elseif (j <= 2.8e-16)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = Float64(j * Float64(fma(i, Float64(y / t), Float64(-c)) * Float64(-t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -1.04e+124], N[(j * N[(c * t + (-N[(y * i), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -5.7e+32], N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6e-221], N[(N[(z * b), $MachinePrecision] * N[(a * N[(i / z), $MachinePrecision] + (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.8e-16], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(N[(i * N[(y / t), $MachinePrecision] + (-c)), $MachinePrecision] * (-t)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.03999999999999994e124

   1. Initial program 75.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\mathsf{neg}\left(i \cdot y\right)\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto j \cdot \color{blue}{\mathsf{fma}\left(c, t, \mathsf{neg}\left(i \cdot y\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \mathsf{neg}\left(\color{blue}{y \cdot i}\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \color{blue}{y \cdot \left(\mathsf{neg}\left(i\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(-1 \cdot i\right)}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \color{blue}{y \cdot \left(-1 \cdot i\right)}\right) \]

      8. neg-mul-1 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(\mathsf{neg}\left(i\right)\right)}\right) \]

      9. lower-neg.f64 79.6

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(-i\right)}\right) \]

   5. Simplified 79.6%

      \[\leadsto \color{blue}{j \cdot \mathsf{fma}\left(c, t, y \cdot \left(-i\right)\right)} \]

   if -1.03999999999999994e124 < j < -5.7e32

   1. Initial program 80.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. lower-*.f64 76.2

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 76.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in c around inf

      \[\leadsto y \cdot \left(z \cdot x\right) + j \cdot \color{blue}{\left(c \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto y \cdot \left(z \cdot x\right) + j \cdot \color{blue}{\left(t \cdot c\right)} \]

      2. lower-*.f64 64.9

         \[\leadsto y \cdot \left(z \cdot x\right) + j \cdot \color{blue}{\left(t \cdot c\right)} \]

   8. Simplified 64.9%

      \[\leadsto y \cdot \left(z \cdot x\right) + j \cdot \color{blue}{\left(t \cdot c\right)} \]

   if -5.7e32 < j < -6.0000000000000003e-221

   1. Initial program 63.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \frac{a \cdot \left(t \cdot x\right)}{z} + \left(x \cdot y + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{z}\right)\right) - \left(-1 \cdot \frac{a \cdot \left(b \cdot i\right)}{z} + b \cdot c\right)\right)} \]

   5. Simplified 58.8%

      \[\leadsto \color{blue}{z \cdot \left(\mathsf{fma}\left(y, x, \frac{\mathsf{fma}\left(j, \mathsf{fma}\left(c, t, y \cdot \left(-i\right)\right), a \cdot \mathsf{fma}\left(t, -x, i \cdot b\right)\right)}{z}\right) - c \cdot b\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(z \cdot \left(\frac{a \cdot i}{z} - c\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(b \cdot z\right) \cdot \left(\frac{a \cdot i}{z} - c\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot z\right) \cdot \left(\frac{a \cdot i}{z} - c\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot z\right)} \cdot \left(\frac{a \cdot i}{z} - c\right) \]

      4. sub-neg N/A

         \[\leadsto \left(b \cdot z\right) \cdot \color{blue}{\left(\frac{a \cdot i}{z} + \left(\mathsf{neg}\left(c\right)\right)\right)} \]

      5. associate-/l* N/A

         \[\leadsto \left(b \cdot z\right) \cdot \left(\color{blue}{a \cdot \frac{i}{z}} + \left(\mathsf{neg}\left(c\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \left(b \cdot z\right) \cdot \left(a \cdot \frac{i}{z} + \color{blue}{-1 \cdot c}\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \left(b \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(a, \frac{i}{z}, -1 \cdot c\right)} \]

      8. lower-/.f64 N/A

         \[\leadsto \left(b \cdot z\right) \cdot \mathsf{fma}\left(a, \color{blue}{\frac{i}{z}}, -1 \cdot c\right) \]

      9. mul-1-neg N/A

         \[\leadsto \left(b \cdot z\right) \cdot \mathsf{fma}\left(a, \frac{i}{z}, \color{blue}{\mathsf{neg}\left(c\right)}\right) \]

      10. lower-neg.f64 57.7

          \[\leadsto \left(b \cdot z\right) \cdot \mathsf{fma}\left(a, \frac{i}{z}, \color{blue}{-c}\right) \]

   8. Simplified 57.7%

      \[\leadsto \color{blue}{\left(b \cdot z\right) \cdot \mathsf{fma}\left(a, \frac{i}{z}, -c\right)} \]

   if -6.0000000000000003e-221 < j < 2.8000000000000001e-16

   1. Initial program 83.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

      2. lower--.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(\color{blue}{y \cdot z} - a \cdot t\right) \]

      4. *-commutative N/A

         \[\leadsto x \cdot \left(y \cdot z - \color{blue}{t \cdot a}\right) \]

      5. lower-*.f64 56.9

         \[\leadsto x \cdot \left(y \cdot z - \color{blue}{t \cdot a}\right) \]

   5. Simplified 56.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right)} \]

   if 2.8000000000000001e-16 < j

   1. Initial program 73.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\mathsf{neg}\left(i \cdot y\right)\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto j \cdot \color{blue}{\mathsf{fma}\left(c, t, \mathsf{neg}\left(i \cdot y\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \mathsf{neg}\left(\color{blue}{y \cdot i}\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \color{blue}{y \cdot \left(\mathsf{neg}\left(i\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(-1 \cdot i\right)}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \color{blue}{y \cdot \left(-1 \cdot i\right)}\right) \]

      8. neg-mul-1 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(\mathsf{neg}\left(i\right)\right)}\right) \]

      9. lower-neg.f64 67.0

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(-i\right)}\right) \]

   5. Simplified 67.0%

      \[\leadsto \color{blue}{j \cdot \mathsf{fma}\left(c, t, y \cdot \left(-i\right)\right)} \]

   6. Taylor expanded in t around -inf

      \[\leadsto j \cdot \color{blue}{\left(-1 \cdot \left(t \cdot \left(-1 \cdot c + \frac{i \cdot y}{t}\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto j \cdot \color{blue}{\left(\mathsf{neg}\left(t \cdot \left(-1 \cdot c + \frac{i \cdot y}{t}\right)\right)\right)} \]

      2. lower-neg.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\mathsf{neg}\left(t \cdot \left(-1 \cdot c + \frac{i \cdot y}{t}\right)\right)\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto j \cdot \left(\mathsf{neg}\left(\color{blue}{t \cdot \left(-1 \cdot c + \frac{i \cdot y}{t}\right)}\right)\right) \]

      4. +-commutative N/A

         \[\leadsto j \cdot \left(\mathsf{neg}\left(t \cdot \color{blue}{\left(\frac{i \cdot y}{t} + -1 \cdot c\right)}\right)\right) \]

      5. associate-/l* N/A

         \[\leadsto j \cdot \left(\mathsf{neg}\left(t \cdot \left(\color{blue}{i \cdot \frac{y}{t}} + -1 \cdot c\right)\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto j \cdot \left(\mathsf{neg}\left(t \cdot \color{blue}{\mathsf{fma}\left(i, \frac{y}{t}, -1 \cdot c\right)}\right)\right) \]

      7. lower-/.f64 N/A

         \[\leadsto j \cdot \left(\mathsf{neg}\left(t \cdot \mathsf{fma}\left(i, \color{blue}{\frac{y}{t}}, -1 \cdot c\right)\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto j \cdot \left(\mathsf{neg}\left(t \cdot \mathsf{fma}\left(i, \frac{y}{t}, \color{blue}{\mathsf{neg}\left(c\right)}\right)\right)\right) \]

      9. lower-neg.f64 70.2

         \[\leadsto j \cdot \left(-t \cdot \mathsf{fma}\left(i, \frac{y}{t}, \color{blue}{-c}\right)\right) \]

   8. Simplified 70.2%

      \[\leadsto j \cdot \color{blue}{\left(-t \cdot \mathsf{fma}\left(i, \frac{y}{t}, -c\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.04 \cdot 10^{+124}:\\ \;\;\;\;j \cdot \mathsf{fma}\left(c, t, -y \cdot i\right)\\ \mathbf{elif}\;j \leq -5.7 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-221}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \mathsf{fma}\left(a, \frac{i}{z}, -c\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(\mathsf{fma}\left(i, \frac{y}{t}, -c\right) \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -7.8 \cdot 10^{+164}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(j, c, x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq -8 \cdot 10^{-230}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot \left(-c\right), b, \mathsf{fma}\left(b, a \cdot i, y \cdot \mathsf{fma}\left(-j, i, x \cdot z\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{+215}:\\ \;\;\;\;\mathsf{fma}\left(x, y \cdot z - t \cdot a, i \cdot \mathsf{fma}\left(j, -y, a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \mathsf{fma}\left(j, t, z \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -7.8e+164)
   (* t (fma j c (* x (- a))))
   (if (<= c -8e-230)
     (fma (* z (- c)) b (fma b (* a i) (* y (fma (- j) i (* x z)))))
     (if (<= c 1.8e+215)
       (fma x (- (* y z) (* t a)) (* i (fma j (- y) (* a b))))
       (* c (fma j t (* z (- b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -7.8e+164) {
		tmp = t * fma(j, c, (x * -a));
	} else if (c <= -8e-230) {
		tmp = fma((z * -c), b, fma(b, (a * i), (y * fma(-j, i, (x * z)))));
	} else if (c <= 1.8e+215) {
		tmp = fma(x, ((y * z) - (t * a)), (i * fma(j, -y, (a * b))));
	} else {
		tmp = c * fma(j, t, (z * -b));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -7.8e+164)
		tmp = Float64(t * fma(j, c, Float64(x * Float64(-a))));
	elseif (c <= -8e-230)
		tmp = fma(Float64(z * Float64(-c)), b, fma(b, Float64(a * i), Float64(y * fma(Float64(-j), i, Float64(x * z)))));
	elseif (c <= 1.8e+215)
		tmp = fma(x, Float64(Float64(y * z) - Float64(t * a)), Float64(i * fma(j, Float64(-y), Float64(a * b))));
	else
		tmp = Float64(c * fma(j, t, Float64(z * Float64(-b))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -7.8e+164], N[(t * N[(j * c + N[(x * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -8e-230], N[(N[(z * (-c)), $MachinePrecision] * b + N[(b * N[(a * i), $MachinePrecision] + N[(y * N[((-j) * i + N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.8e+215], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(i * N[(j * (-y) + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(j * t + N[(z * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if c < -7.79999999999999971e164

   1. Initial program 73.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]

      2. +-commutative N/A

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} + -1 \cdot \left(a \cdot x\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto t \cdot \color{blue}{\mathsf{fma}\left(j, c, -1 \cdot \left(a \cdot x\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto t \cdot \mathsf{fma}\left(j, c, \color{blue}{\mathsf{neg}\left(a \cdot x\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto t \cdot \mathsf{fma}\left(j, c, \color{blue}{a \cdot \left(\mathsf{neg}\left(x\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto t \cdot \mathsf{fma}\left(j, c, a \cdot \color{blue}{\left(-1 \cdot x\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(j, c, \color{blue}{a \cdot \left(-1 \cdot x\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto t \cdot \mathsf{fma}\left(j, c, a \cdot \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \]

      10. lower-neg.f64 68.2

          \[\leadsto t \cdot \mathsf{fma}\left(j, c, a \cdot \color{blue}{\left(-x\right)}\right) \]

   5. Simplified 68.2%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(j, c, a \cdot \left(-x\right)\right)} \]

   if -7.79999999999999971e164 < c < -8.00000000000000037e-230

   1. Initial program 73.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      6. distribute-rgt-in N/A

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, -1 \cdot \left(i \cdot j\right) + x \cdot z, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right)} \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(-1 \cdot i\right) \cdot j} + x \cdot z, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{j \cdot \left(-1 \cdot i\right)} + x \cdot z, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(j, -1 \cdot i, x \cdot z\right)}, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      11. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \color{blue}{\mathsf{neg}\left(i\right)}, x \cdot z\right), \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      12. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \color{blue}{\mathsf{neg}\left(i\right)}, x \cdot z\right), \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), \color{blue}{z \cdot x}\right), \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), \color{blue}{z \cdot x}\right), \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      15. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), \color{blue}{b \cdot \left(\mathsf{neg}\left(\left(c \cdot z - a \cdot i\right)\right)\right)}\right) \]

      16. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), b \cdot \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), \color{blue}{b \cdot \left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)}\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - a \cdot i\right)\right)\right)}\right) \]

      19. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), b \cdot \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z + \left(\mathsf{neg}\left(a \cdot i\right)\right)\right)}\right)\right)\right) \]

   5. Simplified 71.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \mathsf{fma}\left(j, -i, z \cdot x\right), b \cdot \mathsf{fma}\left(c, -z, i \cdot a\right)\right)} \]
   6. Step-by-step derivation

      1. lift-neg.f64 N/A

         \[\leadsto y \cdot \left(j \cdot \color{blue}{\left(\mathsf{neg}\left(i\right)\right)} + z \cdot x\right) + b \cdot \left(c \cdot \left(\mathsf{neg}\left(z\right)\right) + i \cdot a\right) \]

      2. lift-*.f64 N/A

         \[\leadsto y \cdot \left(j \cdot \left(\mathsf{neg}\left(i\right)\right) + \color{blue}{z \cdot x}\right) + b \cdot \left(c \cdot \left(\mathsf{neg}\left(z\right)\right) + i \cdot a\right) \]

      3. lift-fma.f64 N/A

         \[\leadsto y \cdot \color{blue}{\mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right)} + b \cdot \left(c \cdot \left(\mathsf{neg}\left(z\right)\right) + i \cdot a\right) \]

      4. lift-neg.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right) + b \cdot \left(c \cdot \color{blue}{\left(\mathsf{neg}\left(z\right)\right)} + i \cdot a\right) \]

      5. lift-*.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right) + b \cdot \left(c \cdot \left(\mathsf{neg}\left(z\right)\right) + \color{blue}{i \cdot a}\right) \]

      6. lift-fma.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right) + b \cdot \color{blue}{\mathsf{fma}\left(c, \mathsf{neg}\left(z\right), i \cdot a\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right) + \color{blue}{b \cdot \mathsf{fma}\left(c, \mathsf{neg}\left(z\right), i \cdot a\right)} \]

      8. +-commutative N/A

         \[\leadsto \color{blue}{b \cdot \mathsf{fma}\left(c, \mathsf{neg}\left(z\right), i \cdot a\right) + y \cdot \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \mathsf{fma}\left(c, \mathsf{neg}\left(z\right), i \cdot a\right)} + y \cdot \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right) \]

      10. lift-fma.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(\mathsf{neg}\left(z\right)\right) + i \cdot a\right)} + y \cdot \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right) \]

      11. distribute-rgt-in N/A

          \[\leadsto \color{blue}{\left(\left(c \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot b + \left(i \cdot a\right) \cdot b\right)} + y \cdot \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right) \]

      12. associate-+l+ N/A

          \[\leadsto \color{blue}{\left(c \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot b + \left(\left(i \cdot a\right) \cdot b + y \cdot \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right)\right)} \]

      13. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(c \cdot \left(\mathsf{neg}\left(z\right)\right), b, \left(i \cdot a\right) \cdot b + y \cdot \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right)\right)} \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{c \cdot \left(\mathsf{neg}\left(z\right)\right)}, b, \left(i \cdot a\right) \cdot b + y \cdot \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right)\right) \]

   7. Applied egg-rr 74.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c \cdot \left(-z\right), b, \mathsf{fma}\left(b, a \cdot i, y \cdot \mathsf{fma}\left(-j, i, z \cdot x\right)\right)\right)} \]

   if -8.00000000000000037e-230 < c < 1.79999999999999987e215

   1. Initial program 79.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) - \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot i\right)} \]

      2. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) - \color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot \left(b \cdot i\right) \]

      3. cancel-sign-sub N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) + a \cdot \left(b \cdot i\right)} \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - a \cdot t\right) + -1 \cdot \left(i \cdot \left(j \cdot y\right)\right)\right)} + a \cdot \left(b \cdot i\right) \]

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + a \cdot \left(b \cdot i\right)\right)} \]

      6. *-commutative N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(-1 \cdot \color{blue}{\left(\left(j \cdot y\right) \cdot i\right)} + a \cdot \left(b \cdot i\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\color{blue}{\left(-1 \cdot \left(j \cdot y\right)\right) \cdot i} + a \cdot \left(b \cdot i\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(-1 \cdot \left(j \cdot y\right)\right) \cdot i + \color{blue}{\left(a \cdot b\right) \cdot i}\right) \]

      9. distribute-rgt-in N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + a \cdot b\right)} \]

      10. cancel-sign-sub N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot b\right)} \]

      11. mul-1-neg N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-1 \cdot a\right)} \cdot b\right) \]

      12. associate-*r* N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{-1 \cdot \left(a \cdot b\right)}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - a \cdot t, i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)\right)} \]

   5. Simplified 76.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, i \cdot \mathsf{fma}\left(j, -y, b \cdot a\right)\right)} \]

   if 1.79999999999999987e215 < c

   1. Initial program 67.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

      2. sub-neg N/A

         \[\leadsto c \cdot \color{blue}{\left(j \cdot t + \left(\mathsf{neg}\left(b \cdot z\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto c \cdot \left(j \cdot t + \color{blue}{-1 \cdot \left(b \cdot z\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto c \cdot \color{blue}{\mathsf{fma}\left(j, t, -1 \cdot \left(b \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, \color{blue}{\mathsf{neg}\left(b \cdot z\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, \color{blue}{b \cdot \left(\mathsf{neg}\left(z\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, b \cdot \color{blue}{\left(-1 \cdot z\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, \color{blue}{b \cdot \left(-1 \cdot z\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, b \cdot \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right) \]

      10. lower-neg.f64 87.9

          \[\leadsto c \cdot \mathsf{fma}\left(j, t, b \cdot \color{blue}{\left(-z\right)}\right) \]

   5. Simplified 87.9%

      \[\leadsto \color{blue}{c \cdot \mathsf{fma}\left(j, t, b \cdot \left(-z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.8 \cdot 10^{+164}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(j, c, x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq -8 \cdot 10^{-230}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot \left(-c\right), b, \mathsf{fma}\left(b, a \cdot i, y \cdot \mathsf{fma}\left(-j, i, x \cdot z\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{+215}:\\ \;\;\;\;\mathsf{fma}\left(x, y \cdot z - t \cdot a, i \cdot \mathsf{fma}\left(j, -y, a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \mathsf{fma}\left(j, t, z \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -7.8 \cdot 10^{+164}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(j, c, x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq -1.8 \cdot 10^{-84}:\\ \;\;\;\;\mathsf{fma}\left(y, \mathsf{fma}\left(j, -i, x \cdot z\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{+215}:\\ \;\;\;\;\mathsf{fma}\left(x, y \cdot z - t \cdot a, i \cdot \mathsf{fma}\left(j, -y, a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \mathsf{fma}\left(j, t, z \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -7.8e+164)
   (* t (fma j c (* x (- a))))
   (if (<= c -1.8e-84)
     (fma y (fma j (- i) (* x z)) (* b (fma c (- z) (* a i))))
     (if (<= c 1.8e+215)
       (fma x (- (* y z) (* t a)) (* i (fma j (- y) (* a b))))
       (* c (fma j t (* z (- b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -7.8e+164) {
		tmp = t * fma(j, c, (x * -a));
	} else if (c <= -1.8e-84) {
		tmp = fma(y, fma(j, -i, (x * z)), (b * fma(c, -z, (a * i))));
	} else if (c <= 1.8e+215) {
		tmp = fma(x, ((y * z) - (t * a)), (i * fma(j, -y, (a * b))));
	} else {
		tmp = c * fma(j, t, (z * -b));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -7.8e+164)
		tmp = Float64(t * fma(j, c, Float64(x * Float64(-a))));
	elseif (c <= -1.8e-84)
		tmp = fma(y, fma(j, Float64(-i), Float64(x * z)), Float64(b * fma(c, Float64(-z), Float64(a * i))));
	elseif (c <= 1.8e+215)
		tmp = fma(x, Float64(Float64(y * z) - Float64(t * a)), Float64(i * fma(j, Float64(-y), Float64(a * b))));
	else
		tmp = Float64(c * fma(j, t, Float64(z * Float64(-b))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -7.8e+164], N[(t * N[(j * c + N[(x * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.8e-84], N[(y * N[(j * (-i) + N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(c * (-z) + N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.8e+215], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(i * N[(j * (-y) + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(j * t + N[(z * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if c < -7.79999999999999971e164

   1. Initial program 73.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]

      2. +-commutative N/A

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} + -1 \cdot \left(a \cdot x\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto t \cdot \color{blue}{\mathsf{fma}\left(j, c, -1 \cdot \left(a \cdot x\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto t \cdot \mathsf{fma}\left(j, c, \color{blue}{\mathsf{neg}\left(a \cdot x\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto t \cdot \mathsf{fma}\left(j, c, \color{blue}{a \cdot \left(\mathsf{neg}\left(x\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto t \cdot \mathsf{fma}\left(j, c, a \cdot \color{blue}{\left(-1 \cdot x\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(j, c, \color{blue}{a \cdot \left(-1 \cdot x\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto t \cdot \mathsf{fma}\left(j, c, a \cdot \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \]

      10. lower-neg.f64 68.2

          \[\leadsto t \cdot \mathsf{fma}\left(j, c, a \cdot \color{blue}{\left(-x\right)}\right) \]

   5. Simplified 68.2%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(j, c, a \cdot \left(-x\right)\right)} \]

   if -7.79999999999999971e164 < c < -1.80000000000000002e-84

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      6. distribute-rgt-in N/A

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} + \left(\mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, -1 \cdot \left(i \cdot j\right) + x \cdot z, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right)} \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(-1 \cdot i\right) \cdot j} + x \cdot z, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{j \cdot \left(-1 \cdot i\right)} + x \cdot z, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(j, -1 \cdot i, x \cdot z\right)}, \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      11. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \color{blue}{\mathsf{neg}\left(i\right)}, x \cdot z\right), \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      12. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \color{blue}{\mathsf{neg}\left(i\right)}, x \cdot z\right), \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), \color{blue}{z \cdot x}\right), \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), \color{blue}{z \cdot x}\right), \mathsf{neg}\left(b \cdot \left(c \cdot z - a \cdot i\right)\right)\right) \]

      15. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), \color{blue}{b \cdot \left(\mathsf{neg}\left(\left(c \cdot z - a \cdot i\right)\right)\right)}\right) \]

      16. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), b \cdot \color{blue}{\left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), \color{blue}{b \cdot \left(-1 \cdot \left(c \cdot z - a \cdot i\right)\right)}\right) \]

      18. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), b \cdot \color{blue}{\left(\mathsf{neg}\left(\left(c \cdot z - a \cdot i\right)\right)\right)}\right) \]

      19. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(j, \mathsf{neg}\left(i\right), z \cdot x\right), b \cdot \left(\mathsf{neg}\left(\color{blue}{\left(c \cdot z + \left(\mathsf{neg}\left(a \cdot i\right)\right)\right)}\right)\right)\right) \]

   5. Simplified 77.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \mathsf{fma}\left(j, -i, z \cdot x\right), b \cdot \mathsf{fma}\left(c, -z, i \cdot a\right)\right)} \]

   if -1.80000000000000002e-84 < c < 1.79999999999999987e215

   1. Initial program 78.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) - \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot i\right)} \]

      2. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) - \color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot \left(b \cdot i\right) \]

      3. cancel-sign-sub N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) + a \cdot \left(b \cdot i\right)} \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - a \cdot t\right) + -1 \cdot \left(i \cdot \left(j \cdot y\right)\right)\right)} + a \cdot \left(b \cdot i\right) \]

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + a \cdot \left(b \cdot i\right)\right)} \]

      6. *-commutative N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(-1 \cdot \color{blue}{\left(\left(j \cdot y\right) \cdot i\right)} + a \cdot \left(b \cdot i\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\color{blue}{\left(-1 \cdot \left(j \cdot y\right)\right) \cdot i} + a \cdot \left(b \cdot i\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(-1 \cdot \left(j \cdot y\right)\right) \cdot i + \color{blue}{\left(a \cdot b\right) \cdot i}\right) \]

      9. distribute-rgt-in N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + a \cdot b\right)} \]

      10. cancel-sign-sub N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot b\right)} \]

      11. mul-1-neg N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-1 \cdot a\right)} \cdot b\right) \]

      12. associate-*r* N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{-1 \cdot \left(a \cdot b\right)}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - a \cdot t, i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)\right)} \]

   5. Simplified 74.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, i \cdot \mathsf{fma}\left(j, -y, b \cdot a\right)\right)} \]

   if 1.79999999999999987e215 < c

   1. Initial program 67.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

      2. sub-neg N/A

         \[\leadsto c \cdot \color{blue}{\left(j \cdot t + \left(\mathsf{neg}\left(b \cdot z\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto c \cdot \left(j \cdot t + \color{blue}{-1 \cdot \left(b \cdot z\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto c \cdot \color{blue}{\mathsf{fma}\left(j, t, -1 \cdot \left(b \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, \color{blue}{\mathsf{neg}\left(b \cdot z\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, \color{blue}{b \cdot \left(\mathsf{neg}\left(z\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, b \cdot \color{blue}{\left(-1 \cdot z\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, \color{blue}{b \cdot \left(-1 \cdot z\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, b \cdot \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right) \]

      10. lower-neg.f64 87.9

          \[\leadsto c \cdot \mathsf{fma}\left(j, t, b \cdot \color{blue}{\left(-z\right)}\right) \]

   5. Simplified 87.9%

      \[\leadsto \color{blue}{c \cdot \mathsf{fma}\left(j, t, b \cdot \left(-z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.8 \cdot 10^{+164}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(j, c, x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq -1.8 \cdot 10^{-84}:\\ \;\;\;\;\mathsf{fma}\left(y, \mathsf{fma}\left(j, -i, x \cdot z\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{+215}:\\ \;\;\;\;\mathsf{fma}\left(x, y \cdot z - t \cdot a, i \cdot \mathsf{fma}\left(j, -y, a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \mathsf{fma}\left(j, t, z \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, y \cdot z - t \cdot a, i \cdot \mathsf{fma}\left(j, -y, a \cdot b\right)\right)\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-138}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (fma x (- (* y z) (* t a)) (* i (fma j (- y) (* a b))))))
   (if (<= x -2.7e-17)
     t_1
     (if (<= x 3.9e-138) (- (* j (- (* t c) (* y i))) (* c (* z b))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(x, ((y * z) - (t * a)), (i * fma(j, -y, (a * b))));
	double tmp;
	if (x <= -2.7e-17) {
		tmp = t_1;
	} else if (x <= 3.9e-138) {
		tmp = (j * ((t * c) - (y * i))) - (c * (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = fma(x, Float64(Float64(y * z) - Float64(t * a)), Float64(i * fma(j, Float64(-y), Float64(a * b))))
	tmp = 0.0
	if (x <= -2.7e-17)
		tmp = t_1;
	elseif (x <= 3.9e-138)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(c * Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(i * N[(j * (-y) + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.7e-17], t$95$1, If[LessEqual[x, 3.9e-138], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.7000000000000001e-17 or 3.8999999999999999e-138 < x

   1. Initial program 79.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) - \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot i\right)} \]

      2. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) - \color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot \left(b \cdot i\right) \]

      3. cancel-sign-sub N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) + a \cdot \left(b \cdot i\right)} \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - a \cdot t\right) + -1 \cdot \left(i \cdot \left(j \cdot y\right)\right)\right)} + a \cdot \left(b \cdot i\right) \]

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + a \cdot \left(b \cdot i\right)\right)} \]

      6. *-commutative N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(-1 \cdot \color{blue}{\left(\left(j \cdot y\right) \cdot i\right)} + a \cdot \left(b \cdot i\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\color{blue}{\left(-1 \cdot \left(j \cdot y\right)\right) \cdot i} + a \cdot \left(b \cdot i\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \left(\left(-1 \cdot \left(j \cdot y\right)\right) \cdot i + \color{blue}{\left(a \cdot b\right) \cdot i}\right) \]

      9. distribute-rgt-in N/A

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + a \cdot b\right)} \]

      10. cancel-sign-sub N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot b\right)} \]

      11. mul-1-neg N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-1 \cdot a\right)} \cdot b\right) \]

      12. associate-*r* N/A

          \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) + i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{-1 \cdot \left(a \cdot b\right)}\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - a \cdot t, i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)\right)} \]

   5. Simplified 75.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, i \cdot \mathsf{fma}\left(j, -y, b \cdot a\right)\right)} \]

   if -2.7000000000000001e-17 < x < 3.8999999999999999e-138

   1. Initial program 67.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(z \cdot c\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-*r* N/A

         \[\leadsto -1 \cdot \color{blue}{\left(\left(b \cdot z\right) \cdot c\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. associate-*l* N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(b \cdot z\right)\right) \cdot c} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{c \cdot \left(-1 \cdot \left(b \cdot z\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(-1 \cdot \left(b \cdot z\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. mul-1-neg N/A

         \[\leadsto c \cdot \color{blue}{\left(\mathsf{neg}\left(b \cdot z\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto c \cdot \color{blue}{\left(b \cdot \left(\mathsf{neg}\left(z\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      8. mul-1-neg N/A

         \[\leadsto c \cdot \left(b \cdot \color{blue}{\left(-1 \cdot z\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      9. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(b \cdot \left(-1 \cdot z\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      10. mul-1-neg N/A

          \[\leadsto c \cdot \left(b \cdot \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      11. lower-neg.f64 67.1

          \[\leadsto c \cdot \left(b \cdot \color{blue}{\left(-z\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 67.1%

      \[\leadsto \color{blue}{c \cdot \left(b \cdot \left(-z\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(x, y \cdot z - t \cdot a, i \cdot \mathsf{fma}\left(j, -y, a \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-138}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y \cdot z - t \cdot a, i \cdot \mathsf{fma}\left(j, -y, a \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \mathsf{fma}\left(c, t, -y \cdot i\right)\\ \mathbf{if}\;j \leq -1.04 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -5.7 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-221}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \mathsf{fma}\left(a, \frac{i}{z}, -c\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (fma c t (- (* y i))))))
   (if (<= j -1.04e+124)
     t_1
     (if (<= j -5.7e+32)
       (+ (* y (* x z)) (* j (* t c)))
       (if (<= j -6e-221)
         (* (* z b) (fma a (/ i z) (- c)))
         (if (<= j 2.8e-16) (* x (- (* y z) (* t a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * fma(c, t, -(y * i));
	double tmp;
	if (j <= -1.04e+124) {
		tmp = t_1;
	} else if (j <= -5.7e+32) {
		tmp = (y * (x * z)) + (j * (t * c));
	} else if (j <= -6e-221) {
		tmp = (z * b) * fma(a, (i / z), -c);
	} else if (j <= 2.8e-16) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * fma(c, t, Float64(-Float64(y * i))))
	tmp = 0.0
	if (j <= -1.04e+124)
		tmp = t_1;
	elseif (j <= -5.7e+32)
		tmp = Float64(Float64(y * Float64(x * z)) + Float64(j * Float64(t * c)));
	elseif (j <= -6e-221)
		tmp = Float64(Float64(z * b) * fma(a, Float64(i / z), Float64(-c)));
	elseif (j <= 2.8e-16)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(c * t + (-N[(y * i), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.04e+124], t$95$1, If[LessEqual[j, -5.7e+32], N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6e-221], N[(N[(z * b), $MachinePrecision] * N[(a * N[(i / z), $MachinePrecision] + (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.8e-16], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.03999999999999994e124 or 2.8000000000000001e-16 < j

   1. Initial program 74.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\mathsf{neg}\left(i \cdot y\right)\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto j \cdot \color{blue}{\mathsf{fma}\left(c, t, \mathsf{neg}\left(i \cdot y\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \mathsf{neg}\left(\color{blue}{y \cdot i}\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \color{blue}{y \cdot \left(\mathsf{neg}\left(i\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(-1 \cdot i\right)}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \color{blue}{y \cdot \left(-1 \cdot i\right)}\right) \]

      8. neg-mul-1 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(\mathsf{neg}\left(i\right)\right)}\right) \]

      9. lower-neg.f64 72.2

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(-i\right)}\right) \]

   5. Simplified 72.2%

      \[\leadsto \color{blue}{j \cdot \mathsf{fma}\left(c, t, y \cdot \left(-i\right)\right)} \]

   if -1.03999999999999994e124 < j < -5.7e32

   1. Initial program 80.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. lower-*.f64 76.2

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 76.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in c around inf

      \[\leadsto y \cdot \left(z \cdot x\right) + j \cdot \color{blue}{\left(c \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto y \cdot \left(z \cdot x\right) + j \cdot \color{blue}{\left(t \cdot c\right)} \]

      2. lower-*.f64 64.9

         \[\leadsto y \cdot \left(z \cdot x\right) + j \cdot \color{blue}{\left(t \cdot c\right)} \]

   8. Simplified 64.9%

      \[\leadsto y \cdot \left(z \cdot x\right) + j \cdot \color{blue}{\left(t \cdot c\right)} \]

   if -5.7e32 < j < -6.0000000000000003e-221

   1. Initial program 63.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \frac{a \cdot \left(t \cdot x\right)}{z} + \left(x \cdot y + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{z}\right)\right) - \left(-1 \cdot \frac{a \cdot \left(b \cdot i\right)}{z} + b \cdot c\right)\right)} \]

   5. Simplified 58.8%

      \[\leadsto \color{blue}{z \cdot \left(\mathsf{fma}\left(y, x, \frac{\mathsf{fma}\left(j, \mathsf{fma}\left(c, t, y \cdot \left(-i\right)\right), a \cdot \mathsf{fma}\left(t, -x, i \cdot b\right)\right)}{z}\right) - c \cdot b\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(z \cdot \left(\frac{a \cdot i}{z} - c\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(b \cdot z\right) \cdot \left(\frac{a \cdot i}{z} - c\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot z\right) \cdot \left(\frac{a \cdot i}{z} - c\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot z\right)} \cdot \left(\frac{a \cdot i}{z} - c\right) \]

      4. sub-neg N/A

         \[\leadsto \left(b \cdot z\right) \cdot \color{blue}{\left(\frac{a \cdot i}{z} + \left(\mathsf{neg}\left(c\right)\right)\right)} \]

      5. associate-/l* N/A

         \[\leadsto \left(b \cdot z\right) \cdot \left(\color{blue}{a \cdot \frac{i}{z}} + \left(\mathsf{neg}\left(c\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \left(b \cdot z\right) \cdot \left(a \cdot \frac{i}{z} + \color{blue}{-1 \cdot c}\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \left(b \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(a, \frac{i}{z}, -1 \cdot c\right)} \]

      8. lower-/.f64 N/A

         \[\leadsto \left(b \cdot z\right) \cdot \mathsf{fma}\left(a, \color{blue}{\frac{i}{z}}, -1 \cdot c\right) \]

      9. mul-1-neg N/A

         \[\leadsto \left(b \cdot z\right) \cdot \mathsf{fma}\left(a, \frac{i}{z}, \color{blue}{\mathsf{neg}\left(c\right)}\right) \]

      10. lower-neg.f64 57.7

          \[\leadsto \left(b \cdot z\right) \cdot \mathsf{fma}\left(a, \frac{i}{z}, \color{blue}{-c}\right) \]

   8. Simplified 57.7%

      \[\leadsto \color{blue}{\left(b \cdot z\right) \cdot \mathsf{fma}\left(a, \frac{i}{z}, -c\right)} \]

   if -6.0000000000000003e-221 < j < 2.8000000000000001e-16

   1. Initial program 83.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

      2. lower--.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(\color{blue}{y \cdot z} - a \cdot t\right) \]

      4. *-commutative N/A

         \[\leadsto x \cdot \left(y \cdot z - \color{blue}{t \cdot a}\right) \]

      5. lower-*.f64 56.9

         \[\leadsto x \cdot \left(y \cdot z - \color{blue}{t \cdot a}\right) \]

   5. Simplified 56.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.04 \cdot 10^{+124}:\\ \;\;\;\;j \cdot \mathsf{fma}\left(c, t, -y \cdot i\right)\\ \mathbf{elif}\;j \leq -5.7 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-221}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \mathsf{fma}\left(a, \frac{i}{z}, -c\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \mathsf{fma}\left(c, t, -y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot b\right) \cdot \mathsf{fma}\left(a, \frac{i}{z}, -c\right)\\ \mathbf{if}\;b \leq -1.1 \cdot 10^{+117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+103}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z b) (fma a (/ i z) (- c)))))
   (if (<= b -1.1e+117)
     t_1
     (if (<= b 9.2e+103) (+ (* j (- (* t c) (* y i))) (* y (* x z))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * b) * fma(a, (i / z), -c);
	double tmp;
	if (b <= -1.1e+117) {
		tmp = t_1;
	} else if (b <= 9.2e+103) {
		tmp = (j * ((t * c) - (y * i))) + (y * (x * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * b) * fma(a, Float64(i / z), Float64(-c)))
	tmp = 0.0
	if (b <= -1.1e+117)
		tmp = t_1;
	elseif (b <= 9.2e+103)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(y * Float64(x * z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * b), $MachinePrecision] * N[(a * N[(i / z), $MachinePrecision] + (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.1e+117], t$95$1, If[LessEqual[b, 9.2e+103], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.10000000000000007e117 or 9.20000000000000034e103 < b

   1. Initial program 68.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot \frac{a \cdot \left(t \cdot x\right)}{z} + \left(x \cdot y + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{z}\right)\right) - \left(-1 \cdot \frac{a \cdot \left(b \cdot i\right)}{z} + b \cdot c\right)\right)} \]

   5. Simplified 65.0%

      \[\leadsto \color{blue}{z \cdot \left(\mathsf{fma}\left(y, x, \frac{\mathsf{fma}\left(j, \mathsf{fma}\left(c, t, y \cdot \left(-i\right)\right), a \cdot \mathsf{fma}\left(t, -x, i \cdot b\right)\right)}{z}\right) - c \cdot b\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(z \cdot \left(\frac{a \cdot i}{z} - c\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(b \cdot z\right) \cdot \left(\frac{a \cdot i}{z} - c\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot z\right) \cdot \left(\frac{a \cdot i}{z} - c\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot z\right)} \cdot \left(\frac{a \cdot i}{z} - c\right) \]

      4. sub-neg N/A

         \[\leadsto \left(b \cdot z\right) \cdot \color{blue}{\left(\frac{a \cdot i}{z} + \left(\mathsf{neg}\left(c\right)\right)\right)} \]

      5. associate-/l* N/A

         \[\leadsto \left(b \cdot z\right) \cdot \left(\color{blue}{a \cdot \frac{i}{z}} + \left(\mathsf{neg}\left(c\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \left(b \cdot z\right) \cdot \left(a \cdot \frac{i}{z} + \color{blue}{-1 \cdot c}\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \left(b \cdot z\right) \cdot \color{blue}{\mathsf{fma}\left(a, \frac{i}{z}, -1 \cdot c\right)} \]

      8. lower-/.f64 N/A

         \[\leadsto \left(b \cdot z\right) \cdot \mathsf{fma}\left(a, \color{blue}{\frac{i}{z}}, -1 \cdot c\right) \]

      9. mul-1-neg N/A

         \[\leadsto \left(b \cdot z\right) \cdot \mathsf{fma}\left(a, \frac{i}{z}, \color{blue}{\mathsf{neg}\left(c\right)}\right) \]

      10. lower-neg.f64 71.9

          \[\leadsto \left(b \cdot z\right) \cdot \mathsf{fma}\left(a, \frac{i}{z}, \color{blue}{-c}\right) \]

   8. Simplified 71.9%

      \[\leadsto \color{blue}{\left(b \cdot z\right) \cdot \mathsf{fma}\left(a, \frac{i}{z}, -c\right)} \]

   if -1.10000000000000007e117 < b < 9.20000000000000034e103

   1. Initial program 79.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. lower-*.f64 63.1

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 63.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+117}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \mathsf{fma}\left(a, \frac{i}{z}, -c\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+103}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \mathsf{fma}\left(a, \frac{i}{z}, -c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \mathsf{fma}\left(c, t, -y \cdot i\right)\\ \mathbf{if}\;j \leq -1.04 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -2.6 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-298}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(t, -x, b \cdot i\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (fma c t (- (* y i))))))
   (if (<= j -1.04e+124)
     t_1
     (if (<= j -2.6e+30)
       (+ (* y (* x z)) (* j (* t c)))
       (if (<= j 2.3e-298)
         (* a (fma t (- x) (* b i)))
         (if (<= j 2.8e-16) (* x (- (* y z) (* t a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * fma(c, t, -(y * i));
	double tmp;
	if (j <= -1.04e+124) {
		tmp = t_1;
	} else if (j <= -2.6e+30) {
		tmp = (y * (x * z)) + (j * (t * c));
	} else if (j <= 2.3e-298) {
		tmp = a * fma(t, -x, (b * i));
	} else if (j <= 2.8e-16) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * fma(c, t, Float64(-Float64(y * i))))
	tmp = 0.0
	if (j <= -1.04e+124)
		tmp = t_1;
	elseif (j <= -2.6e+30)
		tmp = Float64(Float64(y * Float64(x * z)) + Float64(j * Float64(t * c)));
	elseif (j <= 2.3e-298)
		tmp = Float64(a * fma(t, Float64(-x), Float64(b * i)));
	elseif (j <= 2.8e-16)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(c * t + (-N[(y * i), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.04e+124], t$95$1, If[LessEqual[j, -2.6e+30], N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.3e-298], N[(a * N[(t * (-x) + N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.8e-16], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.03999999999999994e124 or 2.8000000000000001e-16 < j

   1. Initial program 74.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\mathsf{neg}\left(i \cdot y\right)\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto j \cdot \color{blue}{\mathsf{fma}\left(c, t, \mathsf{neg}\left(i \cdot y\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \mathsf{neg}\left(\color{blue}{y \cdot i}\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \color{blue}{y \cdot \left(\mathsf{neg}\left(i\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(-1 \cdot i\right)}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \color{blue}{y \cdot \left(-1 \cdot i\right)}\right) \]

      8. neg-mul-1 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(\mathsf{neg}\left(i\right)\right)}\right) \]

      9. lower-neg.f64 72.2

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(-i\right)}\right) \]

   5. Simplified 72.2%

      \[\leadsto \color{blue}{j \cdot \mathsf{fma}\left(c, t, y \cdot \left(-i\right)\right)} \]

   if -1.03999999999999994e124 < j < -2.59999999999999988e30

   1. Initial program 81.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. lower-*.f64 77.1

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 77.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in c around inf

      \[\leadsto y \cdot \left(z \cdot x\right) + j \cdot \color{blue}{\left(c \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto y \cdot \left(z \cdot x\right) + j \cdot \color{blue}{\left(t \cdot c\right)} \]

      2. lower-*.f64 66.2

         \[\leadsto y \cdot \left(z \cdot x\right) + j \cdot \color{blue}{\left(t \cdot c\right)} \]

   8. Simplified 66.2%

      \[\leadsto y \cdot \left(z \cdot x\right) + j \cdot \color{blue}{\left(t \cdot c\right)} \]

   if -2.59999999999999988e30 < j < 2.3000000000000001e-298

   1. Initial program 71.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(t \cdot x\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{t \cdot \left(\mathsf{neg}\left(x\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(-1 \cdot x\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(t \cdot \left(-1 \cdot x\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(b \cdot i\right)\right)}\right)\right)\right) \]

      7. remove-double-neg N/A

         \[\leadsto a \cdot \left(t \cdot \left(-1 \cdot x\right) + \color{blue}{b \cdot i}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(t, -1 \cdot x, b \cdot i\right)} \]

      9. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(t, \color{blue}{\mathsf{neg}\left(x\right)}, b \cdot i\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(t, \color{blue}{\mathsf{neg}\left(x\right)}, b \cdot i\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(t, \mathsf{neg}\left(x\right), \color{blue}{i \cdot b}\right) \]

      12. lower-*.f64 52.3

          \[\leadsto a \cdot \mathsf{fma}\left(t, -x, \color{blue}{i \cdot b}\right) \]

   5. Simplified 52.3%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(t, -x, i \cdot b\right)} \]

   if 2.3000000000000001e-298 < j < 2.8000000000000001e-16

   1. Initial program 81.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

      2. lower--.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(\color{blue}{y \cdot z} - a \cdot t\right) \]

      4. *-commutative N/A

         \[\leadsto x \cdot \left(y \cdot z - \color{blue}{t \cdot a}\right) \]

      5. lower-*.f64 61.4

         \[\leadsto x \cdot \left(y \cdot z - \color{blue}{t \cdot a}\right) \]

   5. Simplified 61.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.04 \cdot 10^{+124}:\\ \;\;\;\;j \cdot \mathsf{fma}\left(c, t, -y \cdot i\right)\\ \mathbf{elif}\;j \leq -2.6 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-298}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(t, -x, b \cdot i\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \mathsf{fma}\left(c, t, -y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 44.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \mathsf{fma}\left(t, -x, b \cdot i\right)\\ \mathbf{if}\;a \leq -1.3 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.06 \cdot 10^{-287}:\\ \;\;\;\;b \cdot \mathsf{fma}\left(a, i, z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-220}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-78}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (fma t (- x) (* b i)))))
   (if (<= a -1.3e+33)
     t_1
     (if (<= a -2.06e-287)
       (* b (fma a i (* z (- c))))
       (if (<= a 3.2e-220)
         (* c (* t j))
         (if (<= a 9e-78) (* z (* x y)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * fma(t, -x, (b * i));
	double tmp;
	if (a <= -1.3e+33) {
		tmp = t_1;
	} else if (a <= -2.06e-287) {
		tmp = b * fma(a, i, (z * -c));
	} else if (a <= 3.2e-220) {
		tmp = c * (t * j);
	} else if (a <= 9e-78) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * fma(t, Float64(-x), Float64(b * i)))
	tmp = 0.0
	if (a <= -1.3e+33)
		tmp = t_1;
	elseif (a <= -2.06e-287)
		tmp = Float64(b * fma(a, i, Float64(z * Float64(-c))));
	elseif (a <= 3.2e-220)
		tmp = Float64(c * Float64(t * j));
	elseif (a <= 9e-78)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(t * (-x) + N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.3e+33], t$95$1, If[LessEqual[a, -2.06e-287], N[(b * N[(a * i + N[(z * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e-220], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e-78], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.2999999999999999e33 or 9e-78 < a

   1. Initial program 71.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(t \cdot x\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{t \cdot \left(\mathsf{neg}\left(x\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(-1 \cdot x\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(t \cdot \left(-1 \cdot x\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(b \cdot i\right)\right)}\right)\right)\right) \]

      7. remove-double-neg N/A

         \[\leadsto a \cdot \left(t \cdot \left(-1 \cdot x\right) + \color{blue}{b \cdot i}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(t, -1 \cdot x, b \cdot i\right)} \]

      9. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(t, \color{blue}{\mathsf{neg}\left(x\right)}, b \cdot i\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(t, \color{blue}{\mathsf{neg}\left(x\right)}, b \cdot i\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(t, \mathsf{neg}\left(x\right), \color{blue}{i \cdot b}\right) \]

      12. lower-*.f64 56.8

          \[\leadsto a \cdot \mathsf{fma}\left(t, -x, \color{blue}{i \cdot b}\right) \]

   5. Simplified 56.8%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(t, -x, i \cdot b\right)} \]

   if -1.2999999999999999e33 < a < -2.0599999999999999e-287

   1. Initial program 77.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) - \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. mul-1-neg N/A

         \[\leadsto \left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) - \color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot \left(b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. cancel-sign-sub N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) + a \cdot \left(b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(z \cdot \left(x \cdot y - b \cdot c\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} + a \cdot \left(b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(x \cdot y - b \cdot c\right) + \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(b \cdot i\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. cancel-sign-sub N/A

         \[\leadsto \left(z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. associate-*r* N/A

         \[\leadsto \left(z \cdot \left(x \cdot y - b \cdot c\right) + \left(\color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(b \cdot i\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      8. mul-1-neg N/A

         \[\leadsto \left(z \cdot \left(x \cdot y - b \cdot c\right) + \left(\left(-1 \cdot a\right) \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot a\right)} \cdot \left(b \cdot i\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      9. distribute-lft-out-- N/A

         \[\leadsto \left(z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto \left(z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{\left(a \cdot -1\right)} \cdot \left(t \cdot x - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      11. associate-*r* N/A

          \[\leadsto \left(z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      12. distribute-lft-out-- N/A

          \[\leadsto \left(z \cdot \left(x \cdot y - b \cdot c\right) + a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(z, x \cdot y - b \cdot c, a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 71.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \mathsf{fma}\left(c, -b, y \cdot x\right), a \cdot \mathsf{fma}\left(t, -x, i \cdot b\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \left(c \cdot z\right) + a \cdot i\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \left(c \cdot z\right) + a \cdot i\right)} \]

      2. +-commutative N/A

         \[\leadsto b \cdot \color{blue}{\left(a \cdot i + -1 \cdot \left(c \cdot z\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot \color{blue}{\mathsf{fma}\left(a, i, -1 \cdot \left(c \cdot z\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto b \cdot \mathsf{fma}\left(a, i, \color{blue}{\mathsf{neg}\left(c \cdot z\right)}\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto b \cdot \mathsf{fma}\left(a, i, \color{blue}{c \cdot \left(\mathsf{neg}\left(z\right)\right)}\right) \]

      6. mul-1-neg N/A

         \[\leadsto b \cdot \mathsf{fma}\left(a, i, c \cdot \color{blue}{\left(-1 \cdot z\right)}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto b \cdot \mathsf{fma}\left(a, i, \color{blue}{c \cdot \left(-1 \cdot z\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto b \cdot \mathsf{fma}\left(a, i, c \cdot \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right) \]

      9. lower-neg.f64 41.4

         \[\leadsto b \cdot \mathsf{fma}\left(a, i, c \cdot \color{blue}{\left(-z\right)}\right) \]

   8. Simplified 41.4%

      \[\leadsto \color{blue}{b \cdot \mathsf{fma}\left(a, i, c \cdot \left(-z\right)\right)} \]

   if -2.0599999999999999e-287 < a < 3.20000000000000005e-220

   1. Initial program 89.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. lower-*.f64 76.8

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 76.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]

      2. *-commutative N/A

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

      3. lower-*.f64 57.2

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   8. Simplified 57.2%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if 3.20000000000000005e-220 < a < 9e-78

   1. Initial program 81.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

      2. sub-neg N/A

         \[\leadsto z \cdot \color{blue}{\left(x \cdot y + \left(\mathsf{neg}\left(b \cdot c\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto z \cdot \left(x \cdot y + \color{blue}{-1 \cdot \left(b \cdot c\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right) + x \cdot y\right)} \]

      5. associate-*r* N/A

         \[\leadsto z \cdot \left(\color{blue}{\left(-1 \cdot b\right) \cdot c} + x \cdot y\right) \]

      6. *-commutative N/A

         \[\leadsto z \cdot \left(\color{blue}{c \cdot \left(-1 \cdot b\right)} + x \cdot y\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto z \cdot \color{blue}{\mathsf{fma}\left(c, -1 \cdot b, x \cdot y\right)} \]

      8. neg-mul-1 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(b\right)}, x \cdot y\right) \]

      9. lower-neg.f64 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(b\right)}, x \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, \mathsf{neg}\left(b\right), \color{blue}{y \cdot x}\right) \]

      11. lower-*.f64 63.0

          \[\leadsto z \cdot \mathsf{fma}\left(c, -b, \color{blue}{y \cdot x}\right) \]

   5. Simplified 63.0%

      \[\leadsto \color{blue}{z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)} \]

   6. Taylor expanded in c around 0

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 53.6

         \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]

   8. Simplified 53.6%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+33}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(t, -x, b \cdot i\right)\\ \mathbf{elif}\;a \leq -2.06 \cdot 10^{-287}:\\ \;\;\;\;b \cdot \mathsf{fma}\left(a, i, z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-220}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-78}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(t, -x, b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \mathsf{fma}\left(j, -y, a \cdot b\right)\\ \mathbf{if}\;i \leq -3.2 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -6 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(j, c, x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 42000000:\\ \;\;\;\;x \cdot \mathsf{fma}\left(a, -t, y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (fma j (- y) (* a b)))))
   (if (<= i -3.2e+100)
     t_1
     (if (<= i -6e-16)
       (* t (fma j c (* x (- a))))
       (if (<= i 42000000.0) (* x (fma a (- t) (* y z))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * fma(j, -y, (a * b));
	double tmp;
	if (i <= -3.2e+100) {
		tmp = t_1;
	} else if (i <= -6e-16) {
		tmp = t * fma(j, c, (x * -a));
	} else if (i <= 42000000.0) {
		tmp = x * fma(a, -t, (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * fma(j, Float64(-y), Float64(a * b)))
	tmp = 0.0
	if (i <= -3.2e+100)
		tmp = t_1;
	elseif (i <= -6e-16)
		tmp = Float64(t * fma(j, c, Float64(x * Float64(-a))));
	elseif (i <= 42000000.0)
		tmp = Float64(x * fma(a, Float64(-t), Float64(y * z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(j * (-y) + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.2e+100], t$95$1, If[LessEqual[i, -6e-16], N[(t * N[(j * c + N[(x * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 42000000.0], N[(x * N[(a * (-t) + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -3.1999999999999999e100 or 4.2e7 < i

   1. Initial program 70.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot b\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto i \cdot \left(\color{blue}{\left(\mathsf{neg}\left(j \cdot y\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot b\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto i \cdot \left(\color{blue}{j \cdot \left(\mathsf{neg}\left(y\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot b\right)\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(-1 \cdot y\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot b\right)\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto i \cdot \left(j \cdot \left(-1 \cdot y\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(a \cdot b\right)\right)}\right)\right)\right) \]

      7. remove-double-neg N/A

         \[\leadsto i \cdot \left(j \cdot \left(-1 \cdot y\right) + \color{blue}{a \cdot b}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto i \cdot \color{blue}{\mathsf{fma}\left(j, -1 \cdot y, a \cdot b\right)} \]

      9. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(j, \color{blue}{\mathsf{neg}\left(y\right)}, a \cdot b\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto i \cdot \mathsf{fma}\left(j, \color{blue}{\mathsf{neg}\left(y\right)}, a \cdot b\right) \]

      11. *-commutative N/A

          \[\leadsto i \cdot \mathsf{fma}\left(j, \mathsf{neg}\left(y\right), \color{blue}{b \cdot a}\right) \]

      12. lower-*.f64 68.0

          \[\leadsto i \cdot \mathsf{fma}\left(j, -y, \color{blue}{b \cdot a}\right) \]

   5. Simplified 68.0%

      \[\leadsto \color{blue}{i \cdot \mathsf{fma}\left(j, -y, b \cdot a\right)} \]

   if -3.1999999999999999e100 < i < -5.99999999999999987e-16

   1. Initial program 79.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]

      2. +-commutative N/A

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} + -1 \cdot \left(a \cdot x\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto t \cdot \color{blue}{\mathsf{fma}\left(j, c, -1 \cdot \left(a \cdot x\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto t \cdot \mathsf{fma}\left(j, c, \color{blue}{\mathsf{neg}\left(a \cdot x\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto t \cdot \mathsf{fma}\left(j, c, \color{blue}{a \cdot \left(\mathsf{neg}\left(x\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto t \cdot \mathsf{fma}\left(j, c, a \cdot \color{blue}{\left(-1 \cdot x\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(j, c, \color{blue}{a \cdot \left(-1 \cdot x\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto t \cdot \mathsf{fma}\left(j, c, a \cdot \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \]

      10. lower-neg.f64 66.1

          \[\leadsto t \cdot \mathsf{fma}\left(j, c, a \cdot \color{blue}{\left(-x\right)}\right) \]

   5. Simplified 66.1%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(j, c, a \cdot \left(-x\right)\right)} \]

   if -5.99999999999999987e-16 < i < 4.2e7

   1. Initial program 80.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) - \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. mul-1-neg N/A

         \[\leadsto \left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) - \color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot \left(b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. cancel-sign-sub N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) + a \cdot \left(b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(z \cdot \left(x \cdot y - b \cdot c\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} + a \cdot \left(b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(x \cdot y - b \cdot c\right) + \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(b \cdot i\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. cancel-sign-sub N/A

         \[\leadsto \left(z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. associate-*r* N/A

         \[\leadsto \left(z \cdot \left(x \cdot y - b \cdot c\right) + \left(\color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(b \cdot i\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      8. mul-1-neg N/A

         \[\leadsto \left(z \cdot \left(x \cdot y - b \cdot c\right) + \left(\left(-1 \cdot a\right) \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot a\right)} \cdot \left(b \cdot i\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      9. distribute-lft-out-- N/A

         \[\leadsto \left(z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto \left(z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{\left(a \cdot -1\right)} \cdot \left(t \cdot x - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      11. associate-*r* N/A

          \[\leadsto \left(z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      12. distribute-lft-out-- N/A

          \[\leadsto \left(z \cdot \left(x \cdot y - b \cdot c\right) + a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(z, x \cdot y - b \cdot c, a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 79.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \mathsf{fma}\left(c, -b, y \cdot x\right), a \cdot \mathsf{fma}\left(t, -x, i \cdot b\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} \]

      2. mul-1-neg N/A

         \[\leadsto x \cdot \left(\color{blue}{\left(\mathsf{neg}\left(a \cdot t\right)\right)} + y \cdot z\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto x \cdot \left(\color{blue}{a \cdot \left(\mathsf{neg}\left(t\right)\right)} + y \cdot z\right) \]

      4. mul-1-neg N/A

         \[\leadsto x \cdot \left(a \cdot \color{blue}{\left(-1 \cdot t\right)} + y \cdot z\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(a, -1 \cdot t, y \cdot z\right)} \]

      6. mul-1-neg N/A

         \[\leadsto x \cdot \mathsf{fma}\left(a, \color{blue}{\mathsf{neg}\left(t\right)}, y \cdot z\right) \]

      7. lower-neg.f64 N/A

         \[\leadsto x \cdot \mathsf{fma}\left(a, \color{blue}{\mathsf{neg}\left(t\right)}, y \cdot z\right) \]

      8. lower-*.f64 53.8

         \[\leadsto x \cdot \mathsf{fma}\left(a, -t, \color{blue}{y \cdot z}\right) \]

   8. Simplified 53.8%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(a, -t, y \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.2 \cdot 10^{+100}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(j, -y, a \cdot b\right)\\ \mathbf{elif}\;i \leq -6 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(j, c, x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 42000000:\\ \;\;\;\;x \cdot \mathsf{fma}\left(a, -t, y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(j, -y, a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \mathsf{fma}\left(j, -y, a \cdot b\right)\\ \mathbf{if}\;i \leq -3.2 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -6 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(j, c, x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 42000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (fma j (- y) (* a b)))))
   (if (<= i -3.2e+100)
     t_1
     (if (<= i -6e-16)
       (* t (fma j c (* x (- a))))
       (if (<= i 42000000.0) (* x (- (* y z) (* t a))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * fma(j, -y, (a * b));
	double tmp;
	if (i <= -3.2e+100) {
		tmp = t_1;
	} else if (i <= -6e-16) {
		tmp = t * fma(j, c, (x * -a));
	} else if (i <= 42000000.0) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * fma(j, Float64(-y), Float64(a * b)))
	tmp = 0.0
	if (i <= -3.2e+100)
		tmp = t_1;
	elseif (i <= -6e-16)
		tmp = Float64(t * fma(j, c, Float64(x * Float64(-a))));
	elseif (i <= 42000000.0)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(j * (-y) + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.2e+100], t$95$1, If[LessEqual[i, -6e-16], N[(t * N[(j * c + N[(x * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 42000000.0], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -3.1999999999999999e100 or 4.2e7 < i

   1. Initial program 70.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot b\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto i \cdot \left(\color{blue}{\left(\mathsf{neg}\left(j \cdot y\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot b\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto i \cdot \left(\color{blue}{j \cdot \left(\mathsf{neg}\left(y\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot b\right)\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(-1 \cdot y\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot b\right)\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto i \cdot \left(j \cdot \left(-1 \cdot y\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(a \cdot b\right)\right)}\right)\right)\right) \]

      7. remove-double-neg N/A

         \[\leadsto i \cdot \left(j \cdot \left(-1 \cdot y\right) + \color{blue}{a \cdot b}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto i \cdot \color{blue}{\mathsf{fma}\left(j, -1 \cdot y, a \cdot b\right)} \]

      9. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(j, \color{blue}{\mathsf{neg}\left(y\right)}, a \cdot b\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto i \cdot \mathsf{fma}\left(j, \color{blue}{\mathsf{neg}\left(y\right)}, a \cdot b\right) \]

      11. *-commutative N/A

          \[\leadsto i \cdot \mathsf{fma}\left(j, \mathsf{neg}\left(y\right), \color{blue}{b \cdot a}\right) \]

      12. lower-*.f64 68.0

          \[\leadsto i \cdot \mathsf{fma}\left(j, -y, \color{blue}{b \cdot a}\right) \]

   5. Simplified 68.0%

      \[\leadsto \color{blue}{i \cdot \mathsf{fma}\left(j, -y, b \cdot a\right)} \]

   if -3.1999999999999999e100 < i < -5.99999999999999987e-16

   1. Initial program 79.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]

      2. +-commutative N/A

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} + -1 \cdot \left(a \cdot x\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto t \cdot \color{blue}{\mathsf{fma}\left(j, c, -1 \cdot \left(a \cdot x\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto t \cdot \mathsf{fma}\left(j, c, \color{blue}{\mathsf{neg}\left(a \cdot x\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto t \cdot \mathsf{fma}\left(j, c, \color{blue}{a \cdot \left(\mathsf{neg}\left(x\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto t \cdot \mathsf{fma}\left(j, c, a \cdot \color{blue}{\left(-1 \cdot x\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(j, c, \color{blue}{a \cdot \left(-1 \cdot x\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto t \cdot \mathsf{fma}\left(j, c, a \cdot \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \]

      10. lower-neg.f64 66.1

          \[\leadsto t \cdot \mathsf{fma}\left(j, c, a \cdot \color{blue}{\left(-x\right)}\right) \]

   5. Simplified 66.1%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(j, c, a \cdot \left(-x\right)\right)} \]

   if -5.99999999999999987e-16 < i < 4.2e7

   1. Initial program 80.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

      2. lower--.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(\color{blue}{y \cdot z} - a \cdot t\right) \]

      4. *-commutative N/A

         \[\leadsto x \cdot \left(y \cdot z - \color{blue}{t \cdot a}\right) \]

      5. lower-*.f64 53.8

         \[\leadsto x \cdot \left(y \cdot z - \color{blue}{t \cdot a}\right) \]

   5. Simplified 53.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.2 \cdot 10^{+100}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(j, -y, a \cdot b\right)\\ \mathbf{elif}\;i \leq -6 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(j, c, x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 42000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(j, -y, a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.12 \cdot 10^{+134}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -4.2 \cdot 10^{+82}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;i \leq -6.5 \cdot 10^{-16}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -1.12e+134)
   (* i (* y (- j)))
   (if (<= i -4.2e+82)
     (* i (* a b))
     (if (<= i -6.5e-16)
       (* j (* t c))
       (if (<= i 4.2e+42) (* y (* x z)) (* a (* b i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -1.12e+134) {
		tmp = i * (y * -j);
	} else if (i <= -4.2e+82) {
		tmp = i * (a * b);
	} else if (i <= -6.5e-16) {
		tmp = j * (t * c);
	} else if (i <= 4.2e+42) {
		tmp = y * (x * z);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-1.12d+134)) then
        tmp = i * (y * -j)
    else if (i <= (-4.2d+82)) then
        tmp = i * (a * b)
    else if (i <= (-6.5d-16)) then
        tmp = j * (t * c)
    else if (i <= 4.2d+42) then
        tmp = y * (x * z)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -1.12e+134) {
		tmp = i * (y * -j);
	} else if (i <= -4.2e+82) {
		tmp = i * (a * b);
	} else if (i <= -6.5e-16) {
		tmp = j * (t * c);
	} else if (i <= 4.2e+42) {
		tmp = y * (x * z);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -1.12e+134:
		tmp = i * (y * -j)
	elif i <= -4.2e+82:
		tmp = i * (a * b)
	elif i <= -6.5e-16:
		tmp = j * (t * c)
	elif i <= 4.2e+42:
		tmp = y * (x * z)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -1.12e+134)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (i <= -4.2e+82)
		tmp = Float64(i * Float64(a * b));
	elseif (i <= -6.5e-16)
		tmp = Float64(j * Float64(t * c));
	elseif (i <= 4.2e+42)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -1.12e+134)
		tmp = i * (y * -j);
	elseif (i <= -4.2e+82)
		tmp = i * (a * b);
	elseif (i <= -6.5e-16)
		tmp = j * (t * c);
	elseif (i <= 4.2e+42)
		tmp = y * (x * z);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -1.12e+134], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -4.2e+82], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -6.5e-16], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.2e+42], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -1.12000000000000007e134

   1. Initial program 73.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\mathsf{neg}\left(i \cdot y\right)\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto j \cdot \color{blue}{\mathsf{fma}\left(c, t, \mathsf{neg}\left(i \cdot y\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \mathsf{neg}\left(\color{blue}{y \cdot i}\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \color{blue}{y \cdot \left(\mathsf{neg}\left(i\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(-1 \cdot i\right)}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \color{blue}{y \cdot \left(-1 \cdot i\right)}\right) \]

      8. neg-mul-1 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(\mathsf{neg}\left(i\right)\right)}\right) \]

      9. lower-neg.f64 62.3

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(-i\right)}\right) \]

   5. Simplified 62.3%

      \[\leadsto \color{blue}{j \cdot \mathsf{fma}\left(c, t, y \cdot \left(-i\right)\right)} \]

   6. Taylor expanded in c around 0

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(j \cdot y\right)\right)} \]

      2. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{i \cdot \left(\mathsf{neg}\left(j \cdot y\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right)\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto i \cdot \color{blue}{\left(\mathsf{neg}\left(j \cdot y\right)\right)} \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(\mathsf{neg}\left(y\right)\right)\right)} \]

      7. mul-1-neg N/A

         \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(-1 \cdot y\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(-1 \cdot y\right)\right)} \]

      9. mul-1-neg N/A

         \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

      10. lower-neg.f64 50.1

          \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(-y\right)}\right) \]

   8. Simplified 50.1%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(-y\right)\right)} \]

   if -1.12000000000000007e134 < i < -4.2e82

   1. Initial program 64.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(t \cdot x\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{t \cdot \left(\mathsf{neg}\left(x\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(-1 \cdot x\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(t \cdot \left(-1 \cdot x\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(b \cdot i\right)\right)}\right)\right)\right) \]

      7. remove-double-neg N/A

         \[\leadsto a \cdot \left(t \cdot \left(-1 \cdot x\right) + \color{blue}{b \cdot i}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(t, -1 \cdot x, b \cdot i\right)} \]

      9. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(t, \color{blue}{\mathsf{neg}\left(x\right)}, b \cdot i\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(t, \color{blue}{\mathsf{neg}\left(x\right)}, b \cdot i\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(t, \mathsf{neg}\left(x\right), \color{blue}{i \cdot b}\right) \]

      12. lower-*.f64 65.8

          \[\leadsto a \cdot \mathsf{fma}\left(t, -x, \color{blue}{i \cdot b}\right) \]

   5. Simplified 65.8%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(t, -x, i \cdot b\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

      2. lower-*.f64 52.7

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]

   8. Simplified 52.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   9. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(b \cdot a\right)} \cdot i \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot a\right)} \cdot i \]

      4. lower-*.f64 52.7

         \[\leadsto \color{blue}{\left(b \cdot a\right) \cdot i} \]

      5. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot a\right)} \cdot i \]

      6. *-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot b\right)} \cdot i \]

      7. lower-*.f64 52.7

         \[\leadsto \color{blue}{\left(a \cdot b\right)} \cdot i \]

   10. Applied egg-rr 52.7%

       \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]

   if -4.2e82 < i < -6.50000000000000011e-16

   1. Initial program 86.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\mathsf{neg}\left(i \cdot y\right)\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto j \cdot \color{blue}{\mathsf{fma}\left(c, t, \mathsf{neg}\left(i \cdot y\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \mathsf{neg}\left(\color{blue}{y \cdot i}\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \color{blue}{y \cdot \left(\mathsf{neg}\left(i\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(-1 \cdot i\right)}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \color{blue}{y \cdot \left(-1 \cdot i\right)}\right) \]

      8. neg-mul-1 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(\mathsf{neg}\left(i\right)\right)}\right) \]

      9. lower-neg.f64 50.5

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(-i\right)}\right) \]

   5. Simplified 50.5%

      \[\leadsto \color{blue}{j \cdot \mathsf{fma}\left(c, t, y \cdot \left(-i\right)\right)} \]

   6. Taylor expanded in c around inf

      \[\leadsto j \cdot \color{blue}{\left(c \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]

      2. lower-*.f64 50.4

         \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]

   8. Simplified 50.4%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]

   if -6.50000000000000011e-16 < i < 4.19999999999999991e42

   1. Initial program 81.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

      2. sub-neg N/A

         \[\leadsto z \cdot \color{blue}{\left(x \cdot y + \left(\mathsf{neg}\left(b \cdot c\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto z \cdot \left(x \cdot y + \color{blue}{-1 \cdot \left(b \cdot c\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right) + x \cdot y\right)} \]

      5. associate-*r* N/A

         \[\leadsto z \cdot \left(\color{blue}{\left(-1 \cdot b\right) \cdot c} + x \cdot y\right) \]

      6. *-commutative N/A

         \[\leadsto z \cdot \left(\color{blue}{c \cdot \left(-1 \cdot b\right)} + x \cdot y\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto z \cdot \color{blue}{\mathsf{fma}\left(c, -1 \cdot b, x \cdot y\right)} \]

      8. neg-mul-1 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(b\right)}, x \cdot y\right) \]

      9. lower-neg.f64 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(b\right)}, x \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, \mathsf{neg}\left(b\right), \color{blue}{y \cdot x}\right) \]

      11. lower-*.f64 50.7

          \[\leadsto z \cdot \mathsf{fma}\left(c, -b, \color{blue}{y \cdot x}\right) \]

   5. Simplified 50.7%

      \[\leadsto \color{blue}{z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)} \]

   6. Taylor expanded in c around 0

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

      3. associate-*r* N/A

         \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

      5. lower-*.f64 36.0

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]

   8. Simplified 36.0%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

   if 4.19999999999999991e42 < i

   1. Initial program 64.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(t \cdot x\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{t \cdot \left(\mathsf{neg}\left(x\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(-1 \cdot x\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(t \cdot \left(-1 \cdot x\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(b \cdot i\right)\right)}\right)\right)\right) \]

      7. remove-double-neg N/A

         \[\leadsto a \cdot \left(t \cdot \left(-1 \cdot x\right) + \color{blue}{b \cdot i}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(t, -1 \cdot x, b \cdot i\right)} \]

      9. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(t, \color{blue}{\mathsf{neg}\left(x\right)}, b \cdot i\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(t, \color{blue}{\mathsf{neg}\left(x\right)}, b \cdot i\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(t, \mathsf{neg}\left(x\right), \color{blue}{i \cdot b}\right) \]

      12. lower-*.f64 50.6

          \[\leadsto a \cdot \mathsf{fma}\left(t, -x, \color{blue}{i \cdot b}\right) \]

   5. Simplified 50.6%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(t, -x, i \cdot b\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

      2. lower-*.f64 45.3

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]

   8. Simplified 45.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.12 \cdot 10^{+134}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -4.2 \cdot 10^{+82}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;i \leq -6.5 \cdot 10^{-16}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-111}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-260}:\\ \;\;\;\;-x \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+98}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -5.2e-111)
   (* z (* x y))
   (if (<= y 2e-260)
     (- (* x (* t a)))
     (if (<= y 7.5e+98) (* j (* t c)) (* i (* y (- j)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -5.2e-111) {
		tmp = z * (x * y);
	} else if (y <= 2e-260) {
		tmp = -(x * (t * a));
	} else if (y <= 7.5e+98) {
		tmp = j * (t * c);
	} else {
		tmp = i * (y * -j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-5.2d-111)) then
        tmp = z * (x * y)
    else if (y <= 2d-260) then
        tmp = -(x * (t * a))
    else if (y <= 7.5d+98) then
        tmp = j * (t * c)
    else
        tmp = i * (y * -j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -5.2e-111) {
		tmp = z * (x * y);
	} else if (y <= 2e-260) {
		tmp = -(x * (t * a));
	} else if (y <= 7.5e+98) {
		tmp = j * (t * c);
	} else {
		tmp = i * (y * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -5.2e-111:
		tmp = z * (x * y)
	elif y <= 2e-260:
		tmp = -(x * (t * a))
	elif y <= 7.5e+98:
		tmp = j * (t * c)
	else:
		tmp = i * (y * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -5.2e-111)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= 2e-260)
		tmp = Float64(-Float64(x * Float64(t * a)));
	elseif (y <= 7.5e+98)
		tmp = Float64(j * Float64(t * c));
	else
		tmp = Float64(i * Float64(y * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -5.2e-111)
		tmp = z * (x * y);
	elseif (y <= 2e-260)
		tmp = -(x * (t * a));
	elseif (y <= 7.5e+98)
		tmp = j * (t * c);
	else
		tmp = i * (y * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -5.2e-111], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e-260], (-N[(x * N[(t * a), $MachinePrecision]), $MachinePrecision]), If[LessEqual[y, 7.5e+98], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.19999999999999965e-111

   1. Initial program 66.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

      2. sub-neg N/A

         \[\leadsto z \cdot \color{blue}{\left(x \cdot y + \left(\mathsf{neg}\left(b \cdot c\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto z \cdot \left(x \cdot y + \color{blue}{-1 \cdot \left(b \cdot c\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right) + x \cdot y\right)} \]

      5. associate-*r* N/A

         \[\leadsto z \cdot \left(\color{blue}{\left(-1 \cdot b\right) \cdot c} + x \cdot y\right) \]

      6. *-commutative N/A

         \[\leadsto z \cdot \left(\color{blue}{c \cdot \left(-1 \cdot b\right)} + x \cdot y\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto z \cdot \color{blue}{\mathsf{fma}\left(c, -1 \cdot b, x \cdot y\right)} \]

      8. neg-mul-1 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(b\right)}, x \cdot y\right) \]

      9. lower-neg.f64 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(b\right)}, x \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, \mathsf{neg}\left(b\right), \color{blue}{y \cdot x}\right) \]

      11. lower-*.f64 54.9

          \[\leadsto z \cdot \mathsf{fma}\left(c, -b, \color{blue}{y \cdot x}\right) \]

   5. Simplified 54.9%

      \[\leadsto \color{blue}{z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)} \]

   6. Taylor expanded in c around 0

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 44.1

         \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]

   8. Simplified 44.1%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]

   if -5.19999999999999965e-111 < y < 1.99999999999999992e-260

   1. Initial program 86.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(t \cdot x\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{t \cdot \left(\mathsf{neg}\left(x\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(-1 \cdot x\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(t \cdot \left(-1 \cdot x\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(b \cdot i\right)\right)}\right)\right)\right) \]

      7. remove-double-neg N/A

         \[\leadsto a \cdot \left(t \cdot \left(-1 \cdot x\right) + \color{blue}{b \cdot i}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(t, -1 \cdot x, b \cdot i\right)} \]

      9. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(t, \color{blue}{\mathsf{neg}\left(x\right)}, b \cdot i\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(t, \color{blue}{\mathsf{neg}\left(x\right)}, b \cdot i\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(t, \mathsf{neg}\left(x\right), \color{blue}{i \cdot b}\right) \]

      12. lower-*.f64 62.1

          \[\leadsto a \cdot \mathsf{fma}\left(t, -x, \color{blue}{i \cdot b}\right) \]

   5. Simplified 62.1%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(t, -x, i \cdot b\right)} \]
   6. Step-by-step derivation

      1. lift-neg.f64 N/A

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} + i \cdot b\right) \]

      2. lift-*.f64 N/A

         \[\leadsto a \cdot \left(t \cdot \left(\mathsf{neg}\left(x\right)\right) + \color{blue}{i \cdot b}\right) \]

      3. +-commutative N/A

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + t \cdot \left(\mathsf{neg}\left(x\right)\right)\right)} \]

      4. distribute-rgt-in N/A

         \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot a + \left(t \cdot \left(\mathsf{neg}\left(x\right)\right)\right) \cdot a} \]

      5. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(i \cdot b, a, \left(t \cdot \left(\mathsf{neg}\left(x\right)\right)\right) \cdot a\right)} \]

      6. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{i \cdot b}, a, \left(t \cdot \left(\mathsf{neg}\left(x\right)\right)\right) \cdot a\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{b \cdot i}, a, \left(t \cdot \left(\mathsf{neg}\left(x\right)\right)\right) \cdot a\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{b \cdot i}, a, \left(t \cdot \left(\mathsf{neg}\left(x\right)\right)\right) \cdot a\right) \]

      9. lift-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(b \cdot i, a, \left(t \cdot \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \cdot a\right) \]

      10. distribute-rgt-neg-out N/A

          \[\leadsto \mathsf{fma}\left(b \cdot i, a, \color{blue}{\left(\mathsf{neg}\left(t \cdot x\right)\right)} \cdot a\right) \]

      11. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{fma}\left(b \cdot i, a, \color{blue}{\mathsf{neg}\left(\left(t \cdot x\right) \cdot a\right)}\right) \]

      12. lower-neg.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot i, a, \color{blue}{\mathsf{neg}\left(\left(t \cdot x\right) \cdot a\right)}\right) \]

      13. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot i, a, \mathsf{neg}\left(\color{blue}{\left(t \cdot x\right) \cdot a}\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b \cdot i, a, \mathsf{neg}\left(\color{blue}{\left(x \cdot t\right)} \cdot a\right)\right) \]

      15. lower-*.f64 60.0

          \[\leadsto \mathsf{fma}\left(b \cdot i, a, -\color{blue}{\left(x \cdot t\right)} \cdot a\right) \]

   7. Applied egg-rr 60.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot i, a, -\left(x \cdot t\right) \cdot a\right)} \]

   8. Taylor expanded in b around 0

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(a \cdot \left(t \cdot x\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(a \cdot t\right) \cdot x}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{x \cdot \left(a \cdot t\right)}\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{x \cdot \left(\mathsf{neg}\left(a \cdot t\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot t\right)\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right)\right)} \]

      7. associate-*r* N/A

         \[\leadsto x \cdot \color{blue}{\left(\left(-1 \cdot a\right) \cdot t\right)} \]

      8. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{\left(t \cdot \left(-1 \cdot a\right)\right)} \]

      9. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(t \cdot \left(-1 \cdot a\right)\right)} \]

      10. neg-mul-1 N/A

          \[\leadsto x \cdot \left(t \cdot \color{blue}{\left(\mathsf{neg}\left(a\right)\right)}\right) \]

      11. lower-neg.f64 44.0

          \[\leadsto x \cdot \left(t \cdot \color{blue}{\left(-a\right)}\right) \]

   10. Simplified 44.0%

       \[\leadsto \color{blue}{x \cdot \left(t \cdot \left(-a\right)\right)} \]

   if 1.99999999999999992e-260 < y < 7.50000000000000036e98

   1. Initial program 84.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\mathsf{neg}\left(i \cdot y\right)\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto j \cdot \color{blue}{\mathsf{fma}\left(c, t, \mathsf{neg}\left(i \cdot y\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \mathsf{neg}\left(\color{blue}{y \cdot i}\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \color{blue}{y \cdot \left(\mathsf{neg}\left(i\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(-1 \cdot i\right)}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \color{blue}{y \cdot \left(-1 \cdot i\right)}\right) \]

      8. neg-mul-1 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(\mathsf{neg}\left(i\right)\right)}\right) \]

      9. lower-neg.f64 44.5

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(-i\right)}\right) \]

   5. Simplified 44.5%

      \[\leadsto \color{blue}{j \cdot \mathsf{fma}\left(c, t, y \cdot \left(-i\right)\right)} \]

   6. Taylor expanded in c around inf

      \[\leadsto j \cdot \color{blue}{\left(c \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]

      2. lower-*.f64 35.8

         \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]

   8. Simplified 35.8%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]

   if 7.50000000000000036e98 < y

   1. Initial program 65.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\mathsf{neg}\left(i \cdot y\right)\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto j \cdot \color{blue}{\mathsf{fma}\left(c, t, \mathsf{neg}\left(i \cdot y\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \mathsf{neg}\left(\color{blue}{y \cdot i}\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \color{blue}{y \cdot \left(\mathsf{neg}\left(i\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(-1 \cdot i\right)}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \color{blue}{y \cdot \left(-1 \cdot i\right)}\right) \]

      8. neg-mul-1 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(\mathsf{neg}\left(i\right)\right)}\right) \]

      9. lower-neg.f64 49.4

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(-i\right)}\right) \]

   5. Simplified 49.4%

      \[\leadsto \color{blue}{j \cdot \mathsf{fma}\left(c, t, y \cdot \left(-i\right)\right)} \]

   6. Taylor expanded in c around 0

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(j \cdot y\right)\right)} \]

      2. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{i \cdot \left(\mathsf{neg}\left(j \cdot y\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right)\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto i \cdot \color{blue}{\left(\mathsf{neg}\left(j \cdot y\right)\right)} \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(\mathsf{neg}\left(y\right)\right)\right)} \]

      7. mul-1-neg N/A

         \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(-1 \cdot y\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(-1 \cdot y\right)\right)} \]

      9. mul-1-neg N/A

         \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

      10. lower-neg.f64 43.0

          \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(-y\right)}\right) \]

   8. Simplified 43.0%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(-y\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-111}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-260}:\\ \;\;\;\;-x \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+98}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 52.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \mathsf{fma}\left(c, t, -y \cdot i\right)\\ \mathbf{if}\;j \leq -5.8 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{+35}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(t, -x, b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (fma c t (- (* y i))))))
   (if (<= j -5.8e+22)
     t_1
     (if (<= j 3.3e+35) (* a (fma t (- x) (* b i))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * fma(c, t, -(y * i));
	double tmp;
	if (j <= -5.8e+22) {
		tmp = t_1;
	} else if (j <= 3.3e+35) {
		tmp = a * fma(t, -x, (b * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * fma(c, t, Float64(-Float64(y * i))))
	tmp = 0.0
	if (j <= -5.8e+22)
		tmp = t_1;
	elseif (j <= 3.3e+35)
		tmp = Float64(a * fma(t, Float64(-x), Float64(b * i)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(c * t + (-N[(y * i), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5.8e+22], t$95$1, If[LessEqual[j, 3.3e+35], N[(a * N[(t * (-x) + N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if j < -5.8e22 or 3.3000000000000002e35 < j

   1. Initial program 77.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\mathsf{neg}\left(i \cdot y\right)\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto j \cdot \color{blue}{\mathsf{fma}\left(c, t, \mathsf{neg}\left(i \cdot y\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \mathsf{neg}\left(\color{blue}{y \cdot i}\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \color{blue}{y \cdot \left(\mathsf{neg}\left(i\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(-1 \cdot i\right)}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \color{blue}{y \cdot \left(-1 \cdot i\right)}\right) \]

      8. neg-mul-1 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(\mathsf{neg}\left(i\right)\right)}\right) \]

      9. lower-neg.f64 68.6

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(-i\right)}\right) \]

   5. Simplified 68.6%

      \[\leadsto \color{blue}{j \cdot \mathsf{fma}\left(c, t, y \cdot \left(-i\right)\right)} \]

   if -5.8e22 < j < 3.3000000000000002e35

   1. Initial program 74.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(t \cdot x\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{t \cdot \left(\mathsf{neg}\left(x\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(-1 \cdot x\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(t \cdot \left(-1 \cdot x\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(b \cdot i\right)\right)}\right)\right)\right) \]

      7. remove-double-neg N/A

         \[\leadsto a \cdot \left(t \cdot \left(-1 \cdot x\right) + \color{blue}{b \cdot i}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(t, -1 \cdot x, b \cdot i\right)} \]

      9. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(t, \color{blue}{\mathsf{neg}\left(x\right)}, b \cdot i\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(t, \color{blue}{\mathsf{neg}\left(x\right)}, b \cdot i\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(t, \mathsf{neg}\left(x\right), \color{blue}{i \cdot b}\right) \]

      12. lower-*.f64 48.8

          \[\leadsto a \cdot \mathsf{fma}\left(t, -x, \color{blue}{i \cdot b}\right) \]

   5. Simplified 48.8%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(t, -x, i \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.8 \cdot 10^{+22}:\\ \;\;\;\;j \cdot \mathsf{fma}\left(c, t, -y \cdot i\right)\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{+35}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(t, -x, b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \mathsf{fma}\left(c, t, -y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 49.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \mathsf{fma}\left(j, t, z \cdot \left(-b\right)\right)\\ \mathbf{if}\;c \leq -8.2 \cdot 10^{+139}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{+143}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(j, -y, a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (fma j t (* z (- b))))))
   (if (<= c -8.2e+139)
     t_1
     (if (<= c 1.75e+143) (* i (fma j (- y) (* a b))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * fma(j, t, (z * -b));
	double tmp;
	if (c <= -8.2e+139) {
		tmp = t_1;
	} else if (c <= 1.75e+143) {
		tmp = i * fma(j, -y, (a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * fma(j, t, Float64(z * Float64(-b))))
	tmp = 0.0
	if (c <= -8.2e+139)
		tmp = t_1;
	elseif (c <= 1.75e+143)
		tmp = Float64(i * fma(j, Float64(-y), Float64(a * b)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(j * t + N[(z * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -8.2e+139], t$95$1, If[LessEqual[c, 1.75e+143], N[(i * N[(j * (-y) + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if c < -8.2000000000000004e139 or 1.75000000000000004e143 < c

   1. Initial program 68.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

      2. sub-neg N/A

         \[\leadsto c \cdot \color{blue}{\left(j \cdot t + \left(\mathsf{neg}\left(b \cdot z\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto c \cdot \left(j \cdot t + \color{blue}{-1 \cdot \left(b \cdot z\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto c \cdot \color{blue}{\mathsf{fma}\left(j, t, -1 \cdot \left(b \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, \color{blue}{\mathsf{neg}\left(b \cdot z\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, \color{blue}{b \cdot \left(\mathsf{neg}\left(z\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, b \cdot \color{blue}{\left(-1 \cdot z\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, \color{blue}{b \cdot \left(-1 \cdot z\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, b \cdot \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right) \]

      10. lower-neg.f64 72.5

          \[\leadsto c \cdot \mathsf{fma}\left(j, t, b \cdot \color{blue}{\left(-z\right)}\right) \]

   5. Simplified 72.5%

      \[\leadsto \color{blue}{c \cdot \mathsf{fma}\left(j, t, b \cdot \left(-z\right)\right)} \]

   if -8.2000000000000004e139 < c < 1.75000000000000004e143

   1. Initial program 78.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot b\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto i \cdot \left(\color{blue}{\left(\mathsf{neg}\left(j \cdot y\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot b\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto i \cdot \left(\color{blue}{j \cdot \left(\mathsf{neg}\left(y\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot b\right)\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(-1 \cdot y\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(a \cdot b\right)\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto i \cdot \left(j \cdot \left(-1 \cdot y\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(a \cdot b\right)\right)}\right)\right)\right) \]

      7. remove-double-neg N/A

         \[\leadsto i \cdot \left(j \cdot \left(-1 \cdot y\right) + \color{blue}{a \cdot b}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto i \cdot \color{blue}{\mathsf{fma}\left(j, -1 \cdot y, a \cdot b\right)} \]

      9. mul-1-neg N/A

         \[\leadsto i \cdot \mathsf{fma}\left(j, \color{blue}{\mathsf{neg}\left(y\right)}, a \cdot b\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto i \cdot \mathsf{fma}\left(j, \color{blue}{\mathsf{neg}\left(y\right)}, a \cdot b\right) \]

      11. *-commutative N/A

          \[\leadsto i \cdot \mathsf{fma}\left(j, \mathsf{neg}\left(y\right), \color{blue}{b \cdot a}\right) \]

      12. lower-*.f64 49.2

          \[\leadsto i \cdot \mathsf{fma}\left(j, -y, \color{blue}{b \cdot a}\right) \]

   5. Simplified 49.2%

      \[\leadsto \color{blue}{i \cdot \mathsf{fma}\left(j, -y, b \cdot a\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.2 \cdot 10^{+139}:\\ \;\;\;\;c \cdot \mathsf{fma}\left(j, t, z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{+143}:\\ \;\;\;\;i \cdot \mathsf{fma}\left(j, -y, a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \mathsf{fma}\left(j, t, z \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 52.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \mathsf{fma}\left(t, -x, b \cdot i\right)\\ \mathbf{if}\;a \leq -750000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-73}:\\ \;\;\;\;c \cdot \mathsf{fma}\left(j, t, z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (fma t (- x) (* b i)))))
   (if (<= a -750000000000.0)
     t_1
     (if (<= a 1.25e-73) (* c (fma j t (* z (- b)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * fma(t, -x, (b * i));
	double tmp;
	if (a <= -750000000000.0) {
		tmp = t_1;
	} else if (a <= 1.25e-73) {
		tmp = c * fma(j, t, (z * -b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * fma(t, Float64(-x), Float64(b * i)))
	tmp = 0.0
	if (a <= -750000000000.0)
		tmp = t_1;
	elseif (a <= 1.25e-73)
		tmp = Float64(c * fma(j, t, Float64(z * Float64(-b))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(t * (-x) + N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -750000000000.0], t$95$1, If[LessEqual[a, 1.25e-73], N[(c * N[(j * t + N[(z * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -7.5e11 or 1.25e-73 < a

   1. Initial program 71.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(t \cdot x\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{t \cdot \left(\mathsf{neg}\left(x\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(-1 \cdot x\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(t \cdot \left(-1 \cdot x\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(b \cdot i\right)\right)}\right)\right)\right) \]

      7. remove-double-neg N/A

         \[\leadsto a \cdot \left(t \cdot \left(-1 \cdot x\right) + \color{blue}{b \cdot i}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(t, -1 \cdot x, b \cdot i\right)} \]

      9. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(t, \color{blue}{\mathsf{neg}\left(x\right)}, b \cdot i\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(t, \color{blue}{\mathsf{neg}\left(x\right)}, b \cdot i\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(t, \mathsf{neg}\left(x\right), \color{blue}{i \cdot b}\right) \]

      12. lower-*.f64 56.4

          \[\leadsto a \cdot \mathsf{fma}\left(t, -x, \color{blue}{i \cdot b}\right) \]

   5. Simplified 56.4%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(t, -x, i \cdot b\right)} \]

   if -7.5e11 < a < 1.25e-73

   1. Initial program 80.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

      2. sub-neg N/A

         \[\leadsto c \cdot \color{blue}{\left(j \cdot t + \left(\mathsf{neg}\left(b \cdot z\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto c \cdot \left(j \cdot t + \color{blue}{-1 \cdot \left(b \cdot z\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto c \cdot \color{blue}{\mathsf{fma}\left(j, t, -1 \cdot \left(b \cdot z\right)\right)} \]

      5. mul-1-neg N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, \color{blue}{\mathsf{neg}\left(b \cdot z\right)}\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, \color{blue}{b \cdot \left(\mathsf{neg}\left(z\right)\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, b \cdot \color{blue}{\left(-1 \cdot z\right)}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, \color{blue}{b \cdot \left(-1 \cdot z\right)}\right) \]

      9. mul-1-neg N/A

         \[\leadsto c \cdot \mathsf{fma}\left(j, t, b \cdot \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right) \]

      10. lower-neg.f64 49.0

          \[\leadsto c \cdot \mathsf{fma}\left(j, t, b \cdot \color{blue}{\left(-z\right)}\right) \]

   5. Simplified 49.0%

      \[\leadsto \color{blue}{c \cdot \mathsf{fma}\left(j, t, b \cdot \left(-z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -750000000000:\\ \;\;\;\;a \cdot \mathsf{fma}\left(t, -x, b \cdot i\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-73}:\\ \;\;\;\;c \cdot \mathsf{fma}\left(j, t, z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(t, -x, b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 41.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-7}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+122}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(t, -x, b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -7.2e-7)
   (* z (* x y))
   (if (<= y 2.95e+122) (* a (fma t (- x) (* b i))) (* (* y i) (- j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -7.2e-7) {
		tmp = z * (x * y);
	} else if (y <= 2.95e+122) {
		tmp = a * fma(t, -x, (b * i));
	} else {
		tmp = (y * i) * -j;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -7.2e-7)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= 2.95e+122)
		tmp = Float64(a * fma(t, Float64(-x), Float64(b * i)));
	else
		tmp = Float64(Float64(y * i) * Float64(-j));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -7.2e-7], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.95e+122], N[(a * N[(t * (-x) + N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.19999999999999989e-7

   1. Initial program 65.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

      2. sub-neg N/A

         \[\leadsto z \cdot \color{blue}{\left(x \cdot y + \left(\mathsf{neg}\left(b \cdot c\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto z \cdot \left(x \cdot y + \color{blue}{-1 \cdot \left(b \cdot c\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right) + x \cdot y\right)} \]

      5. associate-*r* N/A

         \[\leadsto z \cdot \left(\color{blue}{\left(-1 \cdot b\right) \cdot c} + x \cdot y\right) \]

      6. *-commutative N/A

         \[\leadsto z \cdot \left(\color{blue}{c \cdot \left(-1 \cdot b\right)} + x \cdot y\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto z \cdot \color{blue}{\mathsf{fma}\left(c, -1 \cdot b, x \cdot y\right)} \]

      8. neg-mul-1 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(b\right)}, x \cdot y\right) \]

      9. lower-neg.f64 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(b\right)}, x \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, \mathsf{neg}\left(b\right), \color{blue}{y \cdot x}\right) \]

      11. lower-*.f64 58.0

          \[\leadsto z \cdot \mathsf{fma}\left(c, -b, \color{blue}{y \cdot x}\right) \]

   5. Simplified 58.0%

      \[\leadsto \color{blue}{z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)} \]

   6. Taylor expanded in c around 0

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 48.3

         \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]

   8. Simplified 48.3%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]

   if -7.19999999999999989e-7 < y < 2.95000000000000016e122

   1. Initial program 81.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(t \cdot x\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{t \cdot \left(\mathsf{neg}\left(x\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(-1 \cdot x\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(t \cdot \left(-1 \cdot x\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(b \cdot i\right)\right)}\right)\right)\right) \]

      7. remove-double-neg N/A

         \[\leadsto a \cdot \left(t \cdot \left(-1 \cdot x\right) + \color{blue}{b \cdot i}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(t, -1 \cdot x, b \cdot i\right)} \]

      9. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(t, \color{blue}{\mathsf{neg}\left(x\right)}, b \cdot i\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(t, \color{blue}{\mathsf{neg}\left(x\right)}, b \cdot i\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(t, \mathsf{neg}\left(x\right), \color{blue}{i \cdot b}\right) \]

      12. lower-*.f64 47.8

          \[\leadsto a \cdot \mathsf{fma}\left(t, -x, \color{blue}{i \cdot b}\right) \]

   5. Simplified 47.8%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(t, -x, i \cdot b\right)} \]

   if 2.95000000000000016e122 < y

   1. Initial program 71.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\mathsf{neg}\left(i \cdot y\right)\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto j \cdot \color{blue}{\mathsf{fma}\left(c, t, \mathsf{neg}\left(i \cdot y\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \mathsf{neg}\left(\color{blue}{y \cdot i}\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \color{blue}{y \cdot \left(\mathsf{neg}\left(i\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(-1 \cdot i\right)}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \color{blue}{y \cdot \left(-1 \cdot i\right)}\right) \]

      8. neg-mul-1 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(\mathsf{neg}\left(i\right)\right)}\right) \]

      9. lower-neg.f64 52.9

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(-i\right)}\right) \]

   5. Simplified 52.9%

      \[\leadsto \color{blue}{j \cdot \mathsf{fma}\left(c, t, y \cdot \left(-i\right)\right)} \]

   6. Taylor expanded in c around 0

      \[\leadsto j \cdot \color{blue}{\left(-1 \cdot \left(i \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto j \cdot \color{blue}{\left(\mathsf{neg}\left(i \cdot y\right)\right)} \]

      2. lower-neg.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\mathsf{neg}\left(i \cdot y\right)\right)} \]

      3. lower-*.f64 47.3

         \[\leadsto j \cdot \left(-\color{blue}{i \cdot y}\right) \]

   8. Simplified 47.3%

      \[\leadsto j \cdot \color{blue}{\left(-i \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-7}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+122}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(t, -x, b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.3 \cdot 10^{+101}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;i \leq -6.5 \cdot 10^{-16}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -1.3e+101)
   (* (* y i) (- j))
   (if (<= i -6.5e-16)
     (* j (* t c))
     (if (<= i 4.2e+42) (* y (* x z)) (* a (* b i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -1.3e+101) {
		tmp = (y * i) * -j;
	} else if (i <= -6.5e-16) {
		tmp = j * (t * c);
	} else if (i <= 4.2e+42) {
		tmp = y * (x * z);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-1.3d+101)) then
        tmp = (y * i) * -j
    else if (i <= (-6.5d-16)) then
        tmp = j * (t * c)
    else if (i <= 4.2d+42) then
        tmp = y * (x * z)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -1.3e+101) {
		tmp = (y * i) * -j;
	} else if (i <= -6.5e-16) {
		tmp = j * (t * c);
	} else if (i <= 4.2e+42) {
		tmp = y * (x * z);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -1.3e+101:
		tmp = (y * i) * -j
	elif i <= -6.5e-16:
		tmp = j * (t * c)
	elif i <= 4.2e+42:
		tmp = y * (x * z)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -1.3e+101)
		tmp = Float64(Float64(y * i) * Float64(-j));
	elseif (i <= -6.5e-16)
		tmp = Float64(j * Float64(t * c));
	elseif (i <= 4.2e+42)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -1.3e+101)
		tmp = (y * i) * -j;
	elseif (i <= -6.5e-16)
		tmp = j * (t * c);
	elseif (i <= 4.2e+42)
		tmp = y * (x * z);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -1.3e+101], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[i, -6.5e-16], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.2e+42], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.3e101

   1. Initial program 72.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\mathsf{neg}\left(i \cdot y\right)\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto j \cdot \color{blue}{\mathsf{fma}\left(c, t, \mathsf{neg}\left(i \cdot y\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \mathsf{neg}\left(\color{blue}{y \cdot i}\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \color{blue}{y \cdot \left(\mathsf{neg}\left(i\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(-1 \cdot i\right)}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \color{blue}{y \cdot \left(-1 \cdot i\right)}\right) \]

      8. neg-mul-1 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(\mathsf{neg}\left(i\right)\right)}\right) \]

      9. lower-neg.f64 59.9

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(-i\right)}\right) \]

   5. Simplified 59.9%

      \[\leadsto \color{blue}{j \cdot \mathsf{fma}\left(c, t, y \cdot \left(-i\right)\right)} \]

   6. Taylor expanded in c around 0

      \[\leadsto j \cdot \color{blue}{\left(-1 \cdot \left(i \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto j \cdot \color{blue}{\left(\mathsf{neg}\left(i \cdot y\right)\right)} \]

      2. lower-neg.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\mathsf{neg}\left(i \cdot y\right)\right)} \]

      3. lower-*.f64 47.9

         \[\leadsto j \cdot \left(-\color{blue}{i \cdot y}\right) \]

   8. Simplified 47.9%

      \[\leadsto j \cdot \color{blue}{\left(-i \cdot y\right)} \]

   if -1.3e101 < i < -6.50000000000000011e-16

   1. Initial program 80.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\mathsf{neg}\left(i \cdot y\right)\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto j \cdot \color{blue}{\mathsf{fma}\left(c, t, \mathsf{neg}\left(i \cdot y\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \mathsf{neg}\left(\color{blue}{y \cdot i}\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \color{blue}{y \cdot \left(\mathsf{neg}\left(i\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(-1 \cdot i\right)}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \color{blue}{y \cdot \left(-1 \cdot i\right)}\right) \]

      8. neg-mul-1 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(\mathsf{neg}\left(i\right)\right)}\right) \]

      9. lower-neg.f64 43.5

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(-i\right)}\right) \]

   5. Simplified 43.5%

      \[\leadsto \color{blue}{j \cdot \mathsf{fma}\left(c, t, y \cdot \left(-i\right)\right)} \]

   6. Taylor expanded in c around inf

      \[\leadsto j \cdot \color{blue}{\left(c \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]

      2. lower-*.f64 40.1

         \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]

   8. Simplified 40.1%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]

   if -6.50000000000000011e-16 < i < 4.19999999999999991e42

   1. Initial program 81.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

      2. sub-neg N/A

         \[\leadsto z \cdot \color{blue}{\left(x \cdot y + \left(\mathsf{neg}\left(b \cdot c\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto z \cdot \left(x \cdot y + \color{blue}{-1 \cdot \left(b \cdot c\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right) + x \cdot y\right)} \]

      5. associate-*r* N/A

         \[\leadsto z \cdot \left(\color{blue}{\left(-1 \cdot b\right) \cdot c} + x \cdot y\right) \]

      6. *-commutative N/A

         \[\leadsto z \cdot \left(\color{blue}{c \cdot \left(-1 \cdot b\right)} + x \cdot y\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto z \cdot \color{blue}{\mathsf{fma}\left(c, -1 \cdot b, x \cdot y\right)} \]

      8. neg-mul-1 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(b\right)}, x \cdot y\right) \]

      9. lower-neg.f64 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(b\right)}, x \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, \mathsf{neg}\left(b\right), \color{blue}{y \cdot x}\right) \]

      11. lower-*.f64 50.7

          \[\leadsto z \cdot \mathsf{fma}\left(c, -b, \color{blue}{y \cdot x}\right) \]

   5. Simplified 50.7%

      \[\leadsto \color{blue}{z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)} \]

   6. Taylor expanded in c around 0

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

      3. associate-*r* N/A

         \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

      5. lower-*.f64 36.0

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]

   8. Simplified 36.0%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

   if 4.19999999999999991e42 < i

   1. Initial program 64.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(t \cdot x\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{t \cdot \left(\mathsf{neg}\left(x\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(-1 \cdot x\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(t \cdot \left(-1 \cdot x\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(b \cdot i\right)\right)}\right)\right)\right) \]

      7. remove-double-neg N/A

         \[\leadsto a \cdot \left(t \cdot \left(-1 \cdot x\right) + \color{blue}{b \cdot i}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(t, -1 \cdot x, b \cdot i\right)} \]

      9. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(t, \color{blue}{\mathsf{neg}\left(x\right)}, b \cdot i\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(t, \color{blue}{\mathsf{neg}\left(x\right)}, b \cdot i\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(t, \mathsf{neg}\left(x\right), \color{blue}{i \cdot b}\right) \]

      12. lower-*.f64 50.6

          \[\leadsto a \cdot \mathsf{fma}\left(t, -x, \color{blue}{i \cdot b}\right) \]

   5. Simplified 50.6%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(t, -x, i \cdot b\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

      2. lower-*.f64 45.3

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]

   8. Simplified 45.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.3 \cdot 10^{+101}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;i \leq -6.5 \cdot 10^{-16}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -1.2 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -6.5 \cdot 10^{-16}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* b i))))
   (if (<= i -1.2e+84)
     t_1
     (if (<= i -6.5e-16)
       (* j (* t c))
       (if (<= i 4.2e+42) (* y (* x z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double tmp;
	if (i <= -1.2e+84) {
		tmp = t_1;
	} else if (i <= -6.5e-16) {
		tmp = j * (t * c);
	} else if (i <= 4.2e+42) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * i)
    if (i <= (-1.2d+84)) then
        tmp = t_1
    else if (i <= (-6.5d-16)) then
        tmp = j * (t * c)
    else if (i <= 4.2d+42) then
        tmp = y * (x * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double tmp;
	if (i <= -1.2e+84) {
		tmp = t_1;
	} else if (i <= -6.5e-16) {
		tmp = j * (t * c);
	} else if (i <= 4.2e+42) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (b * i)
	tmp = 0
	if i <= -1.2e+84:
		tmp = t_1
	elif i <= -6.5e-16:
		tmp = j * (t * c)
	elif i <= 4.2e+42:
		tmp = y * (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (i <= -1.2e+84)
		tmp = t_1;
	elseif (i <= -6.5e-16)
		tmp = Float64(j * Float64(t * c));
	elseif (i <= 4.2e+42)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (b * i);
	tmp = 0.0;
	if (i <= -1.2e+84)
		tmp = t_1;
	elseif (i <= -6.5e-16)
		tmp = j * (t * c);
	elseif (i <= 4.2e+42)
		tmp = y * (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.2e+84], t$95$1, If[LessEqual[i, -6.5e-16], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.2e+42], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.2e84 or 4.19999999999999991e42 < i

   1. Initial program 68.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(t \cdot x\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{t \cdot \left(\mathsf{neg}\left(x\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(-1 \cdot x\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(t \cdot \left(-1 \cdot x\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(b \cdot i\right)\right)}\right)\right)\right) \]

      7. remove-double-neg N/A

         \[\leadsto a \cdot \left(t \cdot \left(-1 \cdot x\right) + \color{blue}{b \cdot i}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(t, -1 \cdot x, b \cdot i\right)} \]

      9. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(t, \color{blue}{\mathsf{neg}\left(x\right)}, b \cdot i\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(t, \color{blue}{\mathsf{neg}\left(x\right)}, b \cdot i\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(t, \mathsf{neg}\left(x\right), \color{blue}{i \cdot b}\right) \]

      12. lower-*.f64 49.7

          \[\leadsto a \cdot \mathsf{fma}\left(t, -x, \color{blue}{i \cdot b}\right) \]

   5. Simplified 49.7%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(t, -x, i \cdot b\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

      2. lower-*.f64 42.4

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]

   8. Simplified 42.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if -1.2e84 < i < -6.50000000000000011e-16

   1. Initial program 86.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\mathsf{neg}\left(i \cdot y\right)\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto j \cdot \color{blue}{\mathsf{fma}\left(c, t, \mathsf{neg}\left(i \cdot y\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \mathsf{neg}\left(\color{blue}{y \cdot i}\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \color{blue}{y \cdot \left(\mathsf{neg}\left(i\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(-1 \cdot i\right)}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \color{blue}{y \cdot \left(-1 \cdot i\right)}\right) \]

      8. neg-mul-1 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(\mathsf{neg}\left(i\right)\right)}\right) \]

      9. lower-neg.f64 50.5

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(-i\right)}\right) \]

   5. Simplified 50.5%

      \[\leadsto \color{blue}{j \cdot \mathsf{fma}\left(c, t, y \cdot \left(-i\right)\right)} \]

   6. Taylor expanded in c around inf

      \[\leadsto j \cdot \color{blue}{\left(c \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]

      2. lower-*.f64 50.4

         \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]

   8. Simplified 50.4%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]

   if -6.50000000000000011e-16 < i < 4.19999999999999991e42

   1. Initial program 81.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

      2. sub-neg N/A

         \[\leadsto z \cdot \color{blue}{\left(x \cdot y + \left(\mathsf{neg}\left(b \cdot c\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto z \cdot \left(x \cdot y + \color{blue}{-1 \cdot \left(b \cdot c\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right) + x \cdot y\right)} \]

      5. associate-*r* N/A

         \[\leadsto z \cdot \left(\color{blue}{\left(-1 \cdot b\right) \cdot c} + x \cdot y\right) \]

      6. *-commutative N/A

         \[\leadsto z \cdot \left(\color{blue}{c \cdot \left(-1 \cdot b\right)} + x \cdot y\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto z \cdot \color{blue}{\mathsf{fma}\left(c, -1 \cdot b, x \cdot y\right)} \]

      8. neg-mul-1 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(b\right)}, x \cdot y\right) \]

      9. lower-neg.f64 N/A

         \[\leadsto z \cdot \mathsf{fma}\left(c, \color{blue}{\mathsf{neg}\left(b\right)}, x \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto z \cdot \mathsf{fma}\left(c, \mathsf{neg}\left(b\right), \color{blue}{y \cdot x}\right) \]

      11. lower-*.f64 50.7

          \[\leadsto z \cdot \mathsf{fma}\left(c, -b, \color{blue}{y \cdot x}\right) \]

   5. Simplified 50.7%

      \[\leadsto \color{blue}{z \cdot \mathsf{fma}\left(c, -b, y \cdot x\right)} \]

   6. Taylor expanded in c around 0

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

      3. associate-*r* N/A

         \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

      5. lower-*.f64 36.0

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]

   8. Simplified 36.0%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 21: 29.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -4.5 \cdot 10^{+30}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{+171}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -4.5e+30)
   (* c (* t j))
   (if (<= j 4.2e+171) (* a (* b i)) (* j (* t c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -4.5e+30) {
		tmp = c * (t * j);
	} else if (j <= 4.2e+171) {
		tmp = a * (b * i);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-4.5d+30)) then
        tmp = c * (t * j)
    else if (j <= 4.2d+171) then
        tmp = a * (b * i)
    else
        tmp = j * (t * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -4.5e+30) {
		tmp = c * (t * j);
	} else if (j <= 4.2e+171) {
		tmp = a * (b * i);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -4.5e+30:
		tmp = c * (t * j)
	elif j <= 4.2e+171:
		tmp = a * (b * i)
	else:
		tmp = j * (t * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -4.5e+30)
		tmp = Float64(c * Float64(t * j));
	elseif (j <= 4.2e+171)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(j * Float64(t * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -4.5e+30)
		tmp = c * (t * j);
	elseif (j <= 4.2e+171)
		tmp = a * (b * i);
	else
		tmp = j * (t * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -4.5e+30], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.2e+171], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -4.49999999999999995e30

   1. Initial program 77.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. lower-*.f64 78.1

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 78.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]

      2. *-commutative N/A

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

      3. lower-*.f64 39.0

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   8. Simplified 39.0%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -4.49999999999999995e30 < j < 4.2000000000000003e171

   1. Initial program 74.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(t \cdot x\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{t \cdot \left(\mathsf{neg}\left(x\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(-1 \cdot x\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(t \cdot \left(-1 \cdot x\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(b \cdot i\right)\right)}\right)\right)\right) \]

      7. remove-double-neg N/A

         \[\leadsto a \cdot \left(t \cdot \left(-1 \cdot x\right) + \color{blue}{b \cdot i}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(t, -1 \cdot x, b \cdot i\right)} \]

      9. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(t, \color{blue}{\mathsf{neg}\left(x\right)}, b \cdot i\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(t, \color{blue}{\mathsf{neg}\left(x\right)}, b \cdot i\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(t, \mathsf{neg}\left(x\right), \color{blue}{i \cdot b}\right) \]

      12. lower-*.f64 48.6

          \[\leadsto a \cdot \mathsf{fma}\left(t, -x, \color{blue}{i \cdot b}\right) \]

   5. Simplified 48.6%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(t, -x, i \cdot b\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

      2. lower-*.f64 29.8

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]

   8. Simplified 29.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if 4.2000000000000003e171 < j

   1. Initial program 75.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. sub-neg N/A

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\mathsf{neg}\left(i \cdot y\right)\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto j \cdot \color{blue}{\mathsf{fma}\left(c, t, \mathsf{neg}\left(i \cdot y\right)\right)} \]

      4. *-commutative N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \mathsf{neg}\left(\color{blue}{y \cdot i}\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \color{blue}{y \cdot \left(\mathsf{neg}\left(i\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(-1 \cdot i\right)}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, \color{blue}{y \cdot \left(-1 \cdot i\right)}\right) \]

      8. neg-mul-1 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(\mathsf{neg}\left(i\right)\right)}\right) \]

      9. lower-neg.f64 83.6

         \[\leadsto j \cdot \mathsf{fma}\left(c, t, y \cdot \color{blue}{\left(-i\right)}\right) \]

   5. Simplified 83.6%

      \[\leadsto \color{blue}{j \cdot \mathsf{fma}\left(c, t, y \cdot \left(-i\right)\right)} \]

   6. Taylor expanded in c around inf

      \[\leadsto j \cdot \color{blue}{\left(c \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]

      2. lower-*.f64 47.5

         \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]

   8. Simplified 47.5%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 22: 29.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;j \leq -4.5 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{+171}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))))
   (if (<= j -4.5e+30) t_1 (if (<= j 4.2e+171) (* a (* b i)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (j <= -4.5e+30) {
		tmp = t_1;
	} else if (j <= 4.2e+171) {
		tmp = a * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (t * j)
    if (j <= (-4.5d+30)) then
        tmp = t_1
    else if (j <= 4.2d+171) then
        tmp = a * (b * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (j <= -4.5e+30) {
		tmp = t_1;
	} else if (j <= 4.2e+171) {
		tmp = a * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	tmp = 0
	if j <= -4.5e+30:
		tmp = t_1
	elif j <= 4.2e+171:
		tmp = a * (b * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (j <= -4.5e+30)
		tmp = t_1;
	elseif (j <= 4.2e+171)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	tmp = 0.0;
	if (j <= -4.5e+30)
		tmp = t_1;
	elseif (j <= 4.2e+171)
		tmp = a * (b * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4.5e+30], t$95$1, If[LessEqual[j, 4.2e+171], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if j < -4.49999999999999995e30 or 4.2000000000000003e171 < j

   1. Initial program 77.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. lower-*.f64 78.4

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 78.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]

      2. *-commutative N/A

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

      3. lower-*.f64 41.2

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   8. Simplified 41.2%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -4.49999999999999995e30 < j < 4.2000000000000003e171

   1. Initial program 74.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]

      2. sub-neg N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(t \cdot x\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{t \cdot \left(\mathsf{neg}\left(x\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(-1 \cdot x\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \left(t \cdot \left(-1 \cdot x\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(b \cdot i\right)\right)}\right)\right)\right) \]

      7. remove-double-neg N/A

         \[\leadsto a \cdot \left(t \cdot \left(-1 \cdot x\right) + \color{blue}{b \cdot i}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(t, -1 \cdot x, b \cdot i\right)} \]

      9. mul-1-neg N/A

         \[\leadsto a \cdot \mathsf{fma}\left(t, \color{blue}{\mathsf{neg}\left(x\right)}, b \cdot i\right) \]

      10. lower-neg.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(t, \color{blue}{\mathsf{neg}\left(x\right)}, b \cdot i\right) \]

      11. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(t, \mathsf{neg}\left(x\right), \color{blue}{i \cdot b}\right) \]

      12. lower-*.f64 48.6

          \[\leadsto a \cdot \mathsf{fma}\left(t, -x, \color{blue}{i \cdot b}\right) \]

   5. Simplified 48.6%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(t, -x, i \cdot b\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

      2. lower-*.f64 29.8

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]

   8. Simplified 29.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 22.5% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* b i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (b * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (b * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(b * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (b * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 75.5%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Add Preprocessing

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
4. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]

   2. sub-neg N/A

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right)} \]

   3. mul-1-neg N/A

      \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(t \cdot x\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

   4. distribute-rgt-neg-in N/A

      \[\leadsto a \cdot \left(\color{blue}{t \cdot \left(\mathsf{neg}\left(x\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

   5. mul-1-neg N/A

      \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(-1 \cdot x\right)} + \left(\mathsf{neg}\left(-1 \cdot \left(b \cdot i\right)\right)\right)\right) \]

   6. mul-1-neg N/A

      \[\leadsto a \cdot \left(t \cdot \left(-1 \cdot x\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(b \cdot i\right)\right)}\right)\right)\right) \]

   7. remove-double-neg N/A

      \[\leadsto a \cdot \left(t \cdot \left(-1 \cdot x\right) + \color{blue}{b \cdot i}\right) \]

   8. lower-fma.f64 N/A

      \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(t, -1 \cdot x, b \cdot i\right)} \]

   9. mul-1-neg N/A

      \[\leadsto a \cdot \mathsf{fma}\left(t, \color{blue}{\mathsf{neg}\left(x\right)}, b \cdot i\right) \]

   10. lower-neg.f64 N/A

       \[\leadsto a \cdot \mathsf{fma}\left(t, \color{blue}{\mathsf{neg}\left(x\right)}, b \cdot i\right) \]

   11. *-commutative N/A

       \[\leadsto a \cdot \mathsf{fma}\left(t, \mathsf{neg}\left(x\right), \color{blue}{i \cdot b}\right) \]

   12. lower-*.f64 40.1

       \[\leadsto a \cdot \mathsf{fma}\left(t, -x, \color{blue}{i \cdot b}\right) \]

5. Simplified 40.1%

   \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(t, -x, i \cdot b\right)} \]

6. Taylor expanded in t around 0

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
7. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   2. lower-*.f64 24.9

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]

8. Simplified 24.9%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
9. Add Preprocessing

Developer Target 1: 69.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2024212 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -1015122364899489/125000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -942510763643697/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (if (< t -238547917063487/3125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 10535888557455487/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))